1

COURSES OF STUDIES

For

2014 -2015

Admission Batch

STATISTICS

(M.A. / M.Sc.)

RAVENSHAW UNIVERSITY

CUTTACK

RAVENSHAW UNIVERSITY

2

Syllabus for M.A. / M.Sc. Degree Examination

in Statistics (Semester System)

The course in M.A./M.Sc.(Statistics) shall comprise of sixteen theory papers, each carrying

50 marks and of three hours duration spreading over four semesters (two years). There shall

be one practical paper in each of the first three semesters carrying 100 marks and of six hours

duration, and one project work in the fourth semester carrying 100 marks.

PAPER CODE SUBJECT MARKS

SEMESTER I

ST 1.1.1 Mathematical Analysis 50

ST 1.1.2 Linear Algebra 50

ST 1.1.3 Probability Theory and Distributions-I 50

ST 1.1.4 Statistical Inference-I 50

ST 1.1.5 Practical. 100

SEMESTER II

ST 1.2.6 Probability Theory and Distributions-II 50

ST 1.2.7 Statistical Inference-II 50

ST 1.2.8 Sample Survey Methods 50

ST 1.2.9 Operations Research 50

ST 1.2.10 Practical 100

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SEMESTER III

ST 2.3.11 Multivariate Analysis 50

ST 2.3.12 Design and Analysis of Experiments 50

ST 2.3.13 Demography and Epidemiology 50

ST 2.3.14 Statistical Decision Theory 50

ST 2.3.15 Practical 100

SEMESTER IV

ST 2.4.16 Linear Models and Regression Analysis 50

ST 2.4.17 Stochastic Processes 50

ST 2.4.18 Time Series and Industrial Statistics 50

ST 2.4.19 Elective (any one of the following) 50

A. Advanced Sample Survey Methods

B. Econometrics

C. Advanced Design and Analysis of Experiments

D. Statistical Genetics

E. Actuarial Statistics

F. Quantitative Epidemiology

G. Advanced Operations Research

ST 2.4.20 Project Work 100

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DETAILED SYLLABUS

SEMESTER I

ST 1.1.1 : MATHEMATICAL ANALYSIS

UNIT- I

Limits of sequence, convergence of infinite series, simple tests on convergence. Convergence

of infinite and improper integrals, gamma integral, beta integral and their relationship.

UNIT-II

Metric spaces - limits and metric space, continuous functions in metric spaces,

connectedness, completeness and compactness.

UNIT-III

Sequence and series of functions – point wise convergence, uniform convergence,

consequences of uniform convergence and uniform convergence of series of functions.

UNIT-IV

Differentiation, maxima and minima of functions, functions of several variables. Multiple

integrals and their evaluations by repeated integration, change of variables in multiple

integration.

Text Books

1. Apostal, T.M.: Mathematical Analysis, Narosa Publishing House (Unit I: Chapter 8,

Unit II: Chapters 3 and 4; Unit III: Chapter 9; Unit IV: Chapters 5 and 14)

Reference Books

1. Rudin, W.: Principles of Mathematical Analysis, McGraw-Hill.

2. Goldberg, R.R.: Methods of Real Analysis, Oxford & IBH Publication.

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3. Pati, T.: Functions of a Complex Variable, Pothishala (Private) Limited.

ST 1.1.2: LINEAR ALGEBRA

UNIT-I

Fields, vector spaces, subspaces, linear dependence and independence, basis and dimension

of vector space, completion theorem, vector spaces with an inner product, Gram-Schmidt

orthogonalization process.

UNIT-II

Linear transformations, algebra of matrices, row and column spaces of a matrix, elementary

matrix, determinants, rank and inverse of a matrix, null spaces and nullity, partitioned

matrices, Kronecker product. Hermite canonical form, generalized inverse.

UNIT-III

Real quadratic forms, reduction and classification of quadratic forms, extrema of quadratic

forms, index and signature, triangular reduction of a positive definite matrix.

UNIT-IV

Characteristic roots and vectors, Cayley-Hamilton theorem, algebraic and geometric

multiplicities of a characteristic root, spectral decomposition of a real symmetric matrix.

Text Books

1. Friedberg, S.H. et al. (2010). Linear Algebra. PHI Learning Pvt. Ltd. (Unit I: Chapters

1, 3 and 6; Unit II: Chapters 2 and 3; Unit III: Chapter 6; Unit IV Chapter 5 and 7).

Reference Books

6

1. Graybill, F.E.: Matrices with Applications in Statistics, 2nd

ed., Wadsworth.

2. Rao, C.R.: Linear Statistical Inference and its Application, 2nd

ed., John Wiley &

Sons.

3. Searle, S.R.: Matrix Algebra Useful for Statistics, John Wiley & Sons.

4. Shanti Narayan : A Textbook of Matrices, S. Chand & Co.

ST 1.1.3: PROBABILITY THEORY AND DISTRIBUTIONS – I

UNIT-I

Sequence of sets, limsup, liminf and limit of sequence of sets, classes of sets, field, sigma

field, minimal sigma field, Borel sigma field, set functions. Measure and its properties,

measurable functions and inverse functions. Probability measure, sample space, probability

axioms, properties of probability, conditional probability, Bayes’ theorem, independence of

events.

UNIT-II

Random variables and probability distributions, distribution function of a random variable.

Discrete and continuous random variables, functions of a random variable. Moments,

probability generating and moment generating functions and moment inequalities, Markov,

Holder, Jenson, Liapnov and Chebyshev’s inequalities.

UNIT-III

Random vectors – distribution function of a vector of random variables, joint, marginal and

conditional distributions. Independence of a sequence of random variables. Functions of

random vectors and their distributions. Extreme values and their asymptotic distributions.

Order statistics and their distributions. Conditional expectations.

UNIT-IV

Discrete probability distributions – Degenerate, Uniform, Hypergeometric, Binomial,

Poisson, Negative binomial, Geometric distributions and their properties.

7

Text Books

1. Rohatgi, V.K. and Ehsanes Saleh, A.K.M.: An Introduction to Probability and

Statistics, 2nd

ed., Wiley-Interscience.

2. Gun, A.M., Gupta, M.K. and Dasgupta, B.: Fundamentals of Statistics , Vol.I , World

Press.

Reference Books

1. Bhat, B.R.: Modern Probability Theory, 3rd

ed., New Age International.

3. Gun, A.M., Gupta, M.K. and Dasgupta, B.: An Outline of Statistical Theory, Vol.I

(4th

ed.), World Press.

4. Kingman, J.F.C. and Taylor, S.J.: Introduction to Measure and Probability,

Cambridge University Press.

ST 1.1.4: STATISTICAL INFERENCE – I

UNIT-I

Review of descriptive statistics – detailed study on the interpretation, analysis and

measurements of various numerical characteristics of a frequency distribution.

UNIT-II

Concepts of univariate and bivariate distributions, curve fittings, simple regression and

correlation analysis, rank correlation, correlation ratio, intra-class correlation. Concept of

multivariate distribution, partial and multiple correlations and their properties. Random

sampling, sampling distribution and standard error, standard errors of moments and functions

of moments.

UNIT-III

Parametric models - point estimation, test of hypothesis, concept of interval estimation. Exact

sampling distributions – t, F and chi-square distributions, sampling from bivariate normal

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distribution, distribution of sample correlation coefficient (null case) and regression

coefficient, tests based on t, F and chi-square distributions.

UNIT-IV

Non-parametric tests - single sample and two sample problems, Sign test, Wilcoxon sign

ranked test, run test, median test, Mann-Whitney-Wilcoxon test, Kolmogorov-Smirnov test.

Kruskal – Wallis test, Freedman rank test.

Text Books

1. Sidney Siegel and, N. John Castellan. Nonparametric Statistics for The Behavioral

Sciences, McGraw-Hill.

2. Mukhopadhyaya, P.: Mathematical Statistics, New Central Book Agency, Calcutta.

3. S. C. Gupta and V. K. Kapoor. Fundamentals of Mathematical Statistics, Sultan

Chand and Sons.

Reference Books

1. Gun, A.M., Gupta, M.K. and Dasgupta, B.: An Outline of Statistical Theory, Vol.II

(4th

Edition), World Press.

2. Kale, B.K.: A First Course in Parametric Inference, Narosa Publishing House.

3. Gibbons, J.D.: Nonparametric Inference, McGraw-Hill.

ST 1.1.5: DATA PROCESSING AND C++ LAB.

PART-A

Introduction to computers - application of information technology, computer system and

CPU, input and output devices, secondary storage, systems and application of software

(Window, Dos, Linux).

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PART-B

Use of (i) MS Word and MS Excel, (ii) Statistical software packages

(R/SPSS/CSTAT/MATLAB).

PART-C

Programming using C++:

(i) Simple programs based on C++.

(ii) Frequency distribution, measures of central tendency, dispersion, moments, skewness

and kurtosis.

(iii)Correlation, regression, ranks correlation.

(iv) Test of hypothesis - t and F tests, chi-square test, z test.

(v) Matrices - operations and inversion.

(vi) Determinants - operations and evaluations.

Marks Distributions

Writing programs and operating computers - 80 marks

Viva-voce + Records - 20 marks

References

1. http://www.r-project.org/

2. Lafore, R: Object-Oriented Programming in C++, Sams Publishing.

3. Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T.: Numerical

Recipes in C: The Art of Scientific Computing, Cambridge University Press.

10

SEMESTER II

ST 1.2.6: PROBABILITY THEORY AND DISTRIBUTIONS – II

UNIT-I

Probability distributions – Uniform, Normal, Cauchy, Gamma and Beta distributions and

their properties. Bivariate normal and bivariate hypergeometric distributions. Exponential

family of distributions.

UNIT-II

Convergence on a probability space – convergence in distribution (law), convergence in

probability, convergence in r-th mean, convergence almost surely and their relationships.

UNIT-III

Characteristic function – definition and properties, inversion theorem (without proof),

uniqueness theorem, characteristic function and moments. Convergence of distribution

function and characteristic function. Helly-Bray theorem, Borel-Cantelli lemma.

UNIT-IV

Laws of large numbers – Chebyshev’s, Khinchin’s, and Bernoulli’s laws of large numbers.

Hajek-Reni and Kolmogorov inequalities (statements only) and Kolmogorv’s strong law of

large numbers. Central limit theorem – Lindberg –Levy and Liapounov forms with proofs

and applications. Lindberg-Feller form (without proof).

Reference Books

1. Rohatgi, V.K. and Ehsanes Saleh, A.K.M.: An Introduction to Probability and

Statistics, 2nd

ed., Wiley-Interscience

2. Bhat, B.R.: Modern Probability Theory, 3rd

Edition, New Age International.

3. Gun, A.M., Gupta, M.K. and Dasgupta, B.: An Outline of Statistical Theory, Vol.I

(4th

ed.), World Press.

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ST 1.2.7: STATISTICAL INFERENCE – II

UNIT-I

Information about the parameters as variation in likelihood function, concept of information

and sufficiency, Neyman-Factorizability criterion, likelihood equivalence, minimal sufficient

statistics, exponential family and Pitman family, invariance properties of sufficiency.

Consistent estimation of real and vector valued parameters, invariance of consistent

estimator, consistency of estimators by method of moments and method of percentiles.

Consistent asymptotic normal (CAN) estimator.

UNIT-II

Methods of estimation – maximum likelihood method, method of moments and percentiles,

choice of estimators based on unbiasedness, minimum variance, Rao-Blackwell theorem,

completeness, Lehmann-Scheffe theorem, necessary and sufficient conditions for MVUE,

Cramer-Rao lower bound.

UNIT-III

Test of hypothesis, critical region, test functions, two kinds of errors, size functions, power

functions, Neyman-Pearson lemma, MP, UMP and UMPU tests. Test of composite

hypothesis – similar regions. Likelihood ratio test and its applications.

UNIT-IV

Interval estimation – confidence level, construction of confidence intervals, shortest

confidence intervals, uniformly most accurate one sided confidence intervals, unbiased

confidence intervals.

Reference Books

1. Kale, B.K.: A First Course on Parametric Inference, Narosa Publishing House

12

2. Rohatgi, V.K. and Ehsanes Saleh, A.K.M.: An Introduction to Probability and

Statistics, 2nd

ed., Wiley-Interscience.

3. Gun, A.M., Gupta, M.K. and Dasgupta, B.: An Outline of Statistical Theory, Vol.II,

(4th

ed.), World Press.

ST 1.2.8: SAMPLE SURVEY MERHODS

UNIT-I

Basic concepts of finite population and sampling techniques. Simple random sampling – with

and without replacements, characteristics and methods of selection, estimation of population

mean/total, standard error and its estimate, determination of sample size. Concept of

sampling design, sampling scheme, estimator, sampling strategy, Horvitz-Thompson

estimator of population mean/total and estimate of variance, Yates-Grundy estimator of

variance. Probability proportional to size with replacement – estimation of population

mean/total, variance of the estimator.

UNIT-II

Stratified random sampling – definition, method of selection, estimation of population

mean/total with standard error and its estimate, problems of allocations-proportional and

optimum, comparison with unrestricted sampling.

Systematic sampling – method of selection, estimation of population mean/total, sampling

variance, comparison with simple random sampling and stratified sampling.

UNIT-III

Cluster sampling – equal and unequal size, estimation of population mean/total, standard

error and its estimation, comparison with mean per unit estimator. Two-stage sampling with

equal and unequal first stage units, estimation of population mean/total, standard error and its

estimation, comparison with single-stage sampling.

Double sampling for difference, ratio, regression methods of estimation and stratification.

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UNIT-IV

Use of auxiliary information in sample surveys. Methods of estimation – ratio, product,

difference and regression methods, sampling variance and efficiency of the estimators. Ratio

and regression estimators in stratified sampling. Multivariate ratio estimator (Olkin’s

estimator)

Errors in surveys – Unit and item non-response, effect of unit non-response on the estimate,

methods of studying non-response (call back, without callback and imputation).

Reference Books

1. Cochran, W.G.: Sampling Techniques, 3rd

ed., Wiley

2. Sukhatme, P.V., Sukhatme, B.V., Sukhatme, S. and Asok, C.: Sampling Theory of

Surveys With Applications, Indian Soc. of Agric. Stat., New Delhi

3. Swain, A.K.P.C.: Finite Population Sampling – Theory & Methods, South Asian

Publishers.

ST 1.2.9: OPERATIONS RESEACH

UNIT-I

Definition and scope of operations research, solution to LPP by simplex method, artificial

variables (Big-M and two-phase methods), duality theorem, economic interpretation of

duality. Karmakar interior point algorithm. Transportation and Assignment and problems,

Goal programming.

UNIT-II

Analytical structure of inventory problems, Harris EOQ formula, extension allowing quantity

discounts and shortages, multi-item inventory models, probabilistic inventory problems.

Network scheduling by PERT/CPM. Resource analysis, crashing, project cost, optimization

algorithm, updating.

14

UNIT-III

Simulation model – Monte Carlo simulation, information theory, entropy, expected

information, some properties of channel probabilities. Introduction to fuzzy sets, fuzzy

measures, fuzzy relations, fuzzy set theory and applications.

UNIT-IV

Queueing systems and their characteristics, transient and steady state solutions in poisson

queues.

Reference Books

1. Taha, H.A.: Operational Research: An Introduction, Mc. Millan

2. Kantiswarup, Gupta, P.K. and Man Mohan: Operations Research, Sultan Chand &

Sons

3. Zimermann, H.J.: Fuzzy Set Theory and its Applications, 2nd

ed., Allied Publishers

4. S.D.Sharma: Operational Research: Theory, Methods and Applications, Kedar Nath-

Ram Nath

ST 1.2.10: COMPUTATIONAL STATISTICS LAB. – I

Problems based on:

(i) Estimation Methods

(ii) Testing of Hypothesis

(iii) Sampling Methods

(iv) Operations Research

Marks Distribution

Computational Lab. Work - 80 marks

Viva-Voce + Record - 20 marks

15

SEMESTER III

ST 2.3.11: MULTIVARIATE ANALYSIS

UNIT-I

Multivariate normal distribution – distribution of linear combination of normally distributed

variables, marginal and conditional distributions, distribution of quadratic forms. Random

sampling from normal distribution, maximum likelihood estimators of parameters,

distributions of sample mean vector and matrix of corrected sum of squares and cross

products.

UNIT-II

Estimation of partial and multiple correlation coefficients and their sampling distributions

(null case only). Hotelling’s T2 statistic – properties, distribution and uses, tests on mean

vector for one and more multivariate normal populations and also on equality of the

components of a mean vector in a multivariate normal population. Mahalanobis – D2 statistic

and its use.

UNIT-III

Classification and discrimination procedures – discrimination between two multivariate

normal populations, sample discriminant function, tests associated with discriminant

functions, probabilities of misclassification and their estimation, classification into more than

two multivariate normal populations. Fisher’s dicsriminant function.

UNIT-IV

Wishart matrix – distribution and properties, characteristic function, reproductive property,

marginal and conditional distributions. Distribution of sample generalized variance.

16

Principal components – definition, MLE of principal components and their variances.

Canonical variables and canonical correlations – definition, use, estimation and computation.

Reference Books

1. Anderson, T.W.: An Introduction to Multivariate Statistical Analysis, 2nd

ed., Wiley

2. Morrison, D.F.: Multivariate Statistical Methods, 2nd

ed., McGraw-Hill

3. Rao, C.R.: Linear Statistical Inference and its Applications, 2nd

ed.,Wiley.

ST 2.3.12: DESIGN AND ANALYSIS OF EXPERIMENTS

UNIT-I

Analysis of variance – components and models, analysis of variance of one-way and two-way

fixed and random effect models, variance component estimation and study of various

methods, tests for variance components. Analysis of unbalanced data. Principles of designs of

experiment, experimental error and data interpretation.

UNIT-II

Complete block designs - completely randomized designs, randomized block designs, latin

square designs, Graeco-Latin square designs, cross-over designs. Missing plot techniques –

general theory and applications.

UNIT-III

General factorial experiments, factorial effects, best estimates and testing the significance of

factorial effects, study of 2n, 3

2, 3

3 factorial experiments in randomized blocks. Confounding

in 2n , 3

2 and 3

3 factorial experiments - complete and partial confounding, advantages and

disadvantages, construction and analysis, fractional replication for symmetric factorials.

UNIT-IV

17

Incomplete block designs – balanced incomplete block design, parametric equality and

inequality, intra-block analysis, analysis with recovery of inter-block information. Split plot

and strip plot designs – models and analysis.

Reference Books

1. Das, M.N. and Giri, N.C.: Designs of Experiments, Wiley Eastern.

2. Kempthorne, O.: Design and Analysis of Experiments, Wiley Eastern.

3. Gun, A.M., Gupta, M.K. and Dasgupta, B.: An Outline of Statistical Theory, Vol.II,

(4th

ed.), World Press.

ST 2.3.13: DEMOGRAPHY AND EPIDEMIOLOGY

UNIT-I

Coverage and errors in demographic data, use of balancing equations and Chandrasekharan

Deming formula to check completeness of registration data. Adjustment of age data, use of

Whiples, Mayer and UN indices. Population composition, dependency ratio. Methods of

population projection, use of Leslie matrix. Population distribution, Lorenz curve and Gini

concentration ratio, population pyramid, measures of aging.

Models of population growth, stationary and stable population models, intrinsic rate of

growth, mean length of generation, mean age of stable population, micro models of fertility,

birth interval, models of waiting time, distribution of number of births. Human reproduction

process as a markov renewal process. Population estimation and projection.

UNIT-II

Measures of fertility (period and cohort), measures of reproduction, model age patterns of

fertility, Brass and Coale-Trussel nuptiality rates, SMAM and method of estimation.

Estimation of fertility from age distribution of a population, assessment of fertility from

retrospective enquiry, birth order techniques for defective birth registration data, P/F ratio.

UNIT-III

18

Measures of mortality, Lexis diagram and IMR, life table functions, theories of mortality,

construction of Reed Merell, Greville, Chiang, UN and Coale Demeny model life tables.

Gross and net migrations, measurement of internal migration, international migration:

evaluation and estimation, migration models.

UNIT-IV

Definition and scope of epidemiology, observational epidemiology, experimental

epidemiology, potential error in epidemiological studies. Epidemiology and prevention.

Relative risk and odds ratio, arrangement of 2�2 table. Interpretation of relative risk and odd

ratio, confidence limits, attributable risk. Adjustment of data, direct and indirect adjustments

(without use of multivariate model).

Reference Books

1. Pathak, K.B. and Ram, F.: Techniques of Demography Analysis, Himalayan

Publishers

2. Srinivasan, K.: Basic Demographic Techniques and Applications, Sage Publishers

3. Ramkumar, R.: Technical Demography, Wiley Eastern.

4. Kahn, H.A. and Sempos, C.H.: Statistical Methods in Epidemiology, Oxford

University Press.

5. Beaglehole, R., Bonita, R. and Kjellstrom, T.: Basic Epidemiology, WHO, Geneva,

1993.

ST 2.3.14: STATISTICAL DECISION THEORY

UNIT-I

Game theory and decision theory – composition, decision and risk functions, utility and

subjective probability, randomization. Optimal decision rules – ordering of the decision rules,

geometrical interpretation, form of Bayes’ rules for estimation problem.

UNIT-II

19

Theorems of decision theory – admissibility and completeness, existence and admissibility of

Bayes’ rules, existence of a minimal complete class.

UNIT-III

The separating hyper plane theorem, essential completeness of the class of non-randomised

decision rules, Jensen’s inequality, the minimax theorem, the complete class theorems and

their applications, solving of minimax rules.

UNIT-IV

Sufficient statistics, essential complete class of rules based on sufficient statistics,

exponential families of distributions, complete sufficient statistics and their applications.

Reference Books

1. Ferguson, T.W.: Mathematical Statistics- A Decision Theoretic Approach, Academic

Press.

2. De Groot, M.A.: Optimal Statistical Decision, Mc Graw-Hill

3. Berger, J.O.: Statistical Decision Theory and Bayesian Analysis, Springer-Verlag.

ST 2.3.15: COMPUTATIONAL STATISTICS LAB. –II

Problems based on:

(i) Multivariate Analysis

(ii) Design of Experiments

(iii)Demographic data

(iv) Statistical Decision Theory

(v) Time Series Analysis

(vi) Industrial Statistics

Marks Distribution:

20

Computational Lab. Work - 80 marks

Viva-Voce + Record - 20 marks

SEMESTER IV

ST 2.4.16: LINEAR MODELS AND REGRESSION ANALYSIS

UNIT-I

Regression on the full rank model - methods of estimation and their consequences,

distributional properties, general linear hypothesis, testing of common hypothesis and

reduced models.

UNIT-II

Regression on dummy variables – regression on allocated codes, regression on dummy (0, 1)

variables, use of dummy variables on multiple regression.

UNIT-III

Regression models (not of full rank) – consequences and distributional properties. Estimable

functions – properties, testing for estimability, general linear hypothesis.

UNIT-IV

Selecting the ‘best’ regression equation – all possible regressions, backward and forward

elimination procedures, step-wise regression procedures.

Multiple regression applied to analysis of variance problems – one way and two way

classifications using the models.

Reference Books

1. Searle, S.R.: Linear Models, John Wiley & Sons

2. Draper, N.R. and Smith, H.: Applied Regression Analysis, John Wiley & Sons.

21

ST 2.4.17: STOCHASTIC PROCESSES

UNIT-I

Notations and specification of stochastic process, stationary process, martingales, random

walk and ruin problems, expected duration of the game, generating function of the duration of

the game and for the first passage times, random walk in the plane and space.

UNIT-II

Markov chains - classification of states and chains, and related problems. Determination of

higher transition probabilities, stability of a Markov system, limiting behavior of finite

irreducible chains, ergodic theorem, graph theoretic approach, reducible chains, ergodic

theorem for reducible chains (without proof), finite reducible chains with a single closed class

and with more than one closed class, non homogeneous chains.

UNIT-III

Markov processes with discrete state space – Poisson process, properties of Poisson process,

poison process and related distributions. Generalization of Poisson process – pure birth

process, Yule-Furry process, birth-immigration process, time-dependent Poisson processes,

pure death process, birth and death processes, Erlang process. Champman-Kolmogorov

forward and backward equations,

UNIT-IV

Markov processes with continuous state space – Brownian motion, Wiener process,

differential equations for a Wiener process, Kolmogorov equations, first passage time

distribution for Wiener process.

Reference Books

1. Medhi, J.: Stochastic Processes, Wiley Eastern

2. Feller, W.: An Introduction to Probability Theory and its Applications, Vol.II, Wiley.

3. Karlin, S. and Taylor, H.M.: A First Course In Stochastic Processes, Academic Press.

22

ST 2.4.18 : TIME SERIES AND INDUSTRIAL STATISTICS

UNIT-I

Time series as discrete parameter stochastic process – stationary and non-stationary

stochastic models. Stochastic models and their forecasting - autocorrelation function and

spectrum of stationary process.

UNIT-II

Linear stationary models – general linear process, autoregressive processes, moving average

processes, mixed autoregressive moving average processes. Linear non-stationary models –

autoregressive integrated moving average processes, IMA(0,1,1) process with deterministic

drift, ARIMA processes with added noise.

Forecasting – minimum mean square error forecasts and their properties, calculating and

updating forecasts, forecast functions and forecast weights, use of state space model

formulation, correlation between forecast errors, forecasting in terms of the general weighted

form.

UNIT-III

Industrial statistics – statistical quality control, need for statistical quality control, control

charts in general, random and assignable causes, purpose of control charts, process control,

control charts for measurements, charts for averages, attributes, defectives and defects.

UNIT-IV

Acceptance sampling plans – single and double sampling plans for attributes, producer’s and

consumer’s risk, variable sampling plans, sequential sampling plans. Sequential probability

ratio test- OC and ASN functions, sequential tests for testing means of normal and binomial

populations.

Reference Books

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1. Box, G.E.P., Jenkins, G. M. and Reinsel, G. C.: Time Series Analysis, Pearson

Edition

2. Burr, I.W.: Engineering Statistics and Quality Control, McGraw-Hill

3. Grant, E.L. and Leavenworth, R.S.: Statistical Quality Control, McGraw-Hill.

4. Wald, A.: Sequential Analysis, John Wiley.

ST 2.4.19: ELECTIVE

(Any one of the followings)

A. ADVANCED SAMPLE SURVEY MERHODS

UNIT-I

Unequal probability sampling with replacement – probability proportional to size with

replacement sampling, estimation of mean/total, method of selection, standard error of

estimate and it’s estimation, comparison with SRSWR, gain due to PPSWR sampling,

optimum size measure, estimator based on distinct units in PPSWR sampling

UNIT-II

Unequal probability sampling without replacement – Des Raj’s ordered estimator, Murthy’s

unordered estimator, Horvitv-Thompson estimator and it’s optimal properties. Midzuno,

Narain, Brewer, Durbin, Sampford and Rao-Hartly-Cochran sampling procedures, systematic

sampling with varying probabilities.

Multi-phase Sampling – double sampling for ratio and regression methods, stratification and

PPS sampling. Sampling on two and more occasions.

24

UNIT-III

Problems of finite population inference under a fixed population set up – PDF of data,

Likelihood function, sufficiency, UMVUE, admissibility, average variance under a model,

comparison of strategies. Inference from finite population using prediction theoretic approach

- principle, prediction under polynomial and multiple regression models, predicting a super-

population mean.

UNIT-IV

Errors in surveys – types of errors, mathematical models for measurement error. Problems of

non response – Hansen and Hurwitz technique, Politz-Simon technique. Randomized

response techniques – Warner’s model and unrelated question model. Variance estimation –

methods of random groups, the Jack knife, balanced half sample, and the bootstrap. Small

area estimation – direct, synthetic and composite estimators.

Reference Books

1. Sukhatme, P.V., Sukhatme, B.V., Sukhatme, S. and Asok, C.: Sampling Theory of

Surveys with Applications, Indian Soc. of Agric. Stat., New Delhi

2. Swain, A.K.P.C.: Finite Population Sampling-Theory and Methods, South Asian

Publishers.

3. Hedayat, A.S. and Sinha, B.K.: Design and Inference in Finite Population Sampling,

Wiley-Interscience.

B. ECONOMETRICS

UNIT-I

25

Two variable linear models – assumptions, OLS estimators and their properties, inference,

analysis of variance, prediction. Classical normal linear regression model (CNLRM). k-

variable linear models – OLS estimators and their properties, inference, analysis of variance.

UNIT-II

Multicollinearity-detection, consequences and remedial measures

Heteroscedasticity – nature, OLS estimators in the presence of hteroscedasticity, detection,

consequences and remedial measures. Generalized least squares – GLS estimators (Aitken

estimators), prediction.

UNIT-III

Simultaneous equation models – examples, the simultaneous-equation bias. Identification

problem – concepts and definitions, under, just or exact and over identifications, rules for

identification, test of simultaneity.

UNIT-IV

Simultaneous equation methods – approaches to estimation, method of indirect least squares

(ILS), method of two-stage least squares (2SLS). Stochastic regressors, instrumental

variables.

Reference Books

1. Johnston, J.: Econometric Methods, McGraw-Hill

2. Gujarati, D.: Basic Econometrics, McGraw-Hill.

3. Theil, H.: Introduction to the Theory and Practice of Econometrics, John Wiley.

4. Apte, P.G.: Text Book of Econometrics, Tata McGraw-Hill.

5. Cramer, J.S.: Empirical Econometrics, North Holland.

6. Maddala, G.S.: Econometrics, McGraw-Hill.

C. ADVANCED DESIGN AND ANALYSIS OF EXPERIMENTS

26

UNIT-I

Linear models, estimable functions, estimation and error spaces, best estimates of normal

equations, variance and covariance estimates. Theory of least squares, linear model with

correlated observations, degrees of freedom and sum of squares of linear functions,

distribution of sum of squares, estimate of error sum of squares.

UNIT-II

General properties of block designs – intra block analysis, balancing block structure of

incomplete block designs, recovery of inter block information, optimality of block designs.

Balanced incomplete block designs – properties and analysis, methods of construction.

Lattice designs – analysis. Partially balanced incomplete block designs, association schemes,

intra block analysis

UNIT-III

Factorial experiments – 2n

and 3n . Confounding – construction and method of analysis.

Fractional factorial experiments – construction and analysis. Asymptotic factorial

experiments – analysis.

UNIT-IV

Response surface designs – linear response surface designs, second order response surface

designs. Analysis of covariance – model, normal equations and estimates, sum of squares for

estimates and error, analysis.

Reference Books

1. Joshi, D.D.: Linear Estimation and Design of Experiments, Wiley Eastern.

2. Dey, A.: Theory of Block Designs, Wiley Eastern.

3. Das, M.N. and Giri, N.: Design and Analysis of Experiments, Wiley Eastern

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D. STATISTICAL GENETICS

UNIT-I

Random mating, Hardy-Weinberg law of equilibrium, inbreeding(generation matrix

approach), Concept of gene frequencies, estimation of gene frequencies.

UNIT-II

Statistical analysis for segregation and linkage, single factor segregation, two factor

segregation, heterogeneity of chi-square, detection and estimation of linkage.

UNIT-III

Heritability, repeatability and genetic correlation

UNIT-IV

.Selection and its effect, selection index.

Reference Books

1. Jain and Prabhakaran: Genetics of Population.

2. Narain, P.: Statistical Genetics.

3. Jain: Statistical Techniques in Quantitative Analysis.

4. Narain, Bhatia and Malhotra: Handbook of Statistical Genetics.

5. Mathur, K.: Measurements of Linkage in Heredity.

E. ACTUARIAL STATISTICS

UNIT-I

Mortality – mortality experience, mortality table, graph of Lx, force of mortality, laws of

mortality, mortality table as a population model, expectation of life, stationary funds.

UNIT-II

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Annuities – pure endowments, annuities, accumulations, assurances, varying annuities and

assurances, continuous annuities, family income benefits.

UNIT-III

Policy values – nature of reserve, prospective and retrospective reserves, fractional premiums

and fractional duration, modified reserves, continuous reserves, surrender values and paid up

policies, industrial assurance, children’s deferred assurances, joint life and last survivorship.

UNIT-IV

Contingencies - contingent probabilities, contingent assurances, reversionary annuities,

multiple decrement table, forces of decrement, construction of multiple decrement table.

Pension funds – capital sums on retirement and death, widow’s pension, sickness benefits,

benefits dependent on marriage.

Reference Books

1. Neill, A.: Life Contingencies, Heineman

2. Donald : Compound Interest and Annuities

3. Jordan : Life Contingencies, 2nd

ed.

4. Benjamin and Pollard : Analysis of Mortality and Other Actuarial Statistics

5. Freeman : Finite Differences for Actuarial Students

6. Elandt-Johnson, R.C. and Johnson, N.L.: Survival Models and Data Analysis, Wiley

F. QUANTITATIVE EPIDEMIOLOGY

UNIT-I

Introduction to epidemiology, causation, prevention and commucicable diseases in

epidemiology. Clinical environmental and occupational epidemiology.

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Epidemiologic measures - organizing and presenting epidemiologic data, measures of

disease frequencies, relative risk and odd ratio, attributable risk.

UNIT-II

Analysis of epidemiologic studies – adjustment of data without use of multivariate model,

direct and indirect adjustments. Confounding variables in 2�2 tables, confident limits for

adjusted odd ratios, multiple match controls.

UNIT-III

Regression model, adjustment using multiple regression and multiple logistic models,

survival over several intervals, withdrawals, life table for specific causes, comparison of

complete survival curves. Product limits, Cox regression.

UNIT-IV

Epidemiology of infectious and chronic diseases, epidemiology and cancer prevention.

Environmental epidemiology, molecular and genetic epidemiology.

Reference Books

1. Beaglehole, R., Bonita, B. and Kjellstrom, T.: Basic Epidemiology, WHO

2. Khan, A.K. and Sempos, C.T.: Statistical Methods in Epidemiology, Oxford

University Press

3. Selvin, S.: Statistical Analysis of Epidemiologic Data, Oxford University Press

4. Mc Neil, D.: Epidemiological Research Methods, Wiley & Sons

5. Jakel, J.F., Elmore, J.G. and Katz, D.L.: Epidemiology, Bio-statistics and Preventive

Medicine, WB Saurders Co.

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G. ADVANCED OPERATIONS RESEARCH

UNIT-I

Multi-stage decision processes and dynamic programming. Inter programming branch and

bound algorithm. Stochastic programming, quantile rules, two-stage programming, use of

fractional programming.

UNIT-II

Decision-making in the face of competition, two person games, pure and mixed strategies,

existence of solution and uniqueness of value in zero-sum games, finding solutions in 2x2,

2xm and mxn games. Non-zero sum games, co-operative and competitive games, equilibrium

solutions and their existence in bi-matrix games. Nash equilibrium solution.

UNIT-III

s-S policy for inventory and its derivation in the case of exponential demand, multi-echelon

inventory models, models with variable supply and model for perishable items, estimation of

EOQ in some simple cases.

UNIT-IV

Transient solution of M/M/1 queue, bulk queue (bulk arrival and bulk service), finite queues,

queues in tandem, G1/G/1 queue and its solution, simulation of queues. Flows in networks,

max-flow min-cut theorem.

Replacement problems, block and age replacement policies, dynamic programming approach

for maintenance problems, replacement of items with long life, project management.

Reference Books

1. Hardly, G.: Non-linear and Dynamic Programming, Addison Wesley

2. Murthy, K.G.: Linear and Combinatorial Programming, John Wiley

3. Kleeiniock, L.: Queueing Systems Theory, Vol.I, John Wiley

4. Saaty, T.L.: Elements of Queueing Theory with Applications, McGraw Hill

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5. Hadley, G. and Whitin, T.M.: Analysis of Inventory Systems, Prentice Hall

6. Starr, M.K. and Miller, D.W.: Inventory Control-Theory and Practice, Prentice Hall

7. Mckinsey, J.C.C.: Introduction to the Theory of Games, McGraw Hill

8. Wagner, H.M.: Principles of Operations Research with Applications to Managerial

Decisions, Prentice Hall

9. Gross, D. and Harris, C.M.: Fundamentals of Queueing Theory, John Wiley

H. RESEARCH METHODOLOGY (detailed syllabus attached)

UNIT-I

What is Research Methodology, Different types of research: - problem solving research,

Applied and basic research, Scientific research, Research and the scientific method, Business

research, Good research, Scientific method in good research.

Different stages of Research process

Concept of sample and sampling in research, sample frame, sample size, sampling methods.

UNIT-II

Designing the study: Sampling design, Questionnaire, Resource Allocation& budgets,

Evaluation methods, Pilot testing, Data collection, Analysis & interpretation, Reporting,

Analysis.

Research proposal: The purpose, Research benefits, Types of research proposals. Evaluating

the research proposal.

Types of studies: Exploratory Studies : Qualitative Techniques.

UNIT-III

Secondary data analysis,

Univariate, bivariate and multivariate techniques of data analysis,

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Hypothesis testing: t, z, chi-square& ANOVA, correlation, regression, non-parametric

techniques, Cluster analysis and Factor analysis ( to discuss only the concept and

application).

Descriptive Studies: Causal studies: concept, testing causal hypothesis, exploring secondary

data.

UNIT-IV

Survey methods: Communicating with participants: personal interview, evaluation of

personal interview, increasing non-response error, reducing non-response error, observational

studies, analysis and presentation of data, editing, coding, data entry

(Small projects – study and presentation by students in groups of 2 or 3 )

Reference Books

1. C. R. Kothari: Research Methodology: Methods & Technology, New Age Int. Publ.

2. Gupta Gupta : Research Methodology: Texts and cases with SPSS Application (2011

edn.), International Book House, New Delhi.

3. A. K. P. C. Swain : A Text Book of Research Methodology, Kalyani Publishers.

4. Naresh Malhotra : Marketing Research, Pearson.

ST 2.4.20: PROJECT WORK

Project work will be based on the review of literature on a particular topic, or based on either

primary or secondary data collected by the student attached either to any of the faculty

members or any eminent statistician working in any statistical organization of the state.

Report of the project work, neatly typed and in a soft bound form with a certificate from the

supervisor will be submitted for examination.

Marks Distribution

Project writing - 70 marks

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Viva-voce - 30 marks