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Administrivia Introduction Outline
Functional Data Analysis
Venue: Tuesday/Thursday1:25 - 2:40WN 145
Lecturer: Giles Hooker
Office Hours: Wednesday 2 - 4Comstock 1186Ph: 5-1638e-mail: gjh27
Administrivia Introduction Outline
Texts and Resources
Ramsay and Silverman, 2007,"Functional Data Analysis",Springerwww.functionaldata.org
Other Books:Eubank, 1996, "Nonparametric Regression and Spline Smoothing"Wahba, 1990, "Spline Models for Observational Data"Ferraty and Vieu, 2006, "Nonparametric Functional Data Analysis"Berlinet and Thomas-Agnan, 2004, "Reproducing Kernel HilbertSpaces in Probability and Statistics"
Administrivia Introduction Outline
Background Expectations
Prerequisites: BTRY 601, 602 and ORIE 670
Really: Basic probability, theoretical statistics, linear algebra,multivariate calculus, programming.
Helpful: Multivariate statistics, functional analysis, differentialequations.
Administrivia Introduction Outline
Software
Matlab:
www.mathworks.com/academia/student_center/www.cit.cornell.edu/labs/software.html
fdaM toolbox (www.functionaldata.org)
FDA toolbox also available for R/S-Plus
I do not assume familiarity with Matlab, but some knowledge ofprogramming may be helpful.
Administrivia Introduction Outline
Assessment
3 assignments (15% each)In class discussion (15%)Brumback and Rice, 1998, "Smoothing Spline Models for theAnalysis of Nested and Crossed Samples of Curves", JASA,with discussion.Cuevas, Febrero and Fraiman, 2004, "An ANOVA Test forFunctional Data", CSDA.Class project (40%)See Lecture 3
Administrivia Introduction Outline
What is Functional Data?
Measures of position of nib of a pen when writing "fda". 20replications, measurements taken at 200 hertz.
Administrivia Introduction Outline
Characteristics
Data are measurements of smooth processes over timeWe usually do not want to make parametric assumptionsabout those processes.Often have multiple measurements of the same processWe are interested in describing the variation of processes.Frequently, collected data have high resolution and low noise.Can be applied to any estimate of a smooth process.
Administrivia Introduction Outline
Data may be measured more noisily
Average daily precipitation in Vancouver, BC
Administrivia Introduction Outline
Data may exhibit multiple modes of variation
Nondurable goods index. Monthly readings 1940-2000.
Administrivia Introduction Outline
A More Complicated Scenario
Data are low noise butlow-resolutionMeasured at unequalintervalsWe know that the curvesmust be monotone
Administrivia Introduction Outline
Salient Features May Be Rates of Change
Administrivia Introduction Outline
Variation Is Not Always Vertical
Administrivia Introduction Outline
And also:
binary datacount datadensity estimationbivariate/multivariate data
Administrivia Introduction Outline
What is Functional Data Analysis?
Analysis of data that are viewed as smooth curvesModes of variation between curvesDiscrimination between curvesUsing curves to predict other quantities (and vice versa)Making use of derivatives as data
Administrivia Introduction Outline
Smoothing
How, when, how much, properties:
Administrivia Introduction Outline
Analysis of Multiple Curves
Modes of variation
First and second principle components of handwriting data.
Administrivia Introduction Outline
Inference About Treatement
Boys vs Girls
Administrivia Introduction Outline
Relate Curves To Other Quantities
Scalars predicted from curves:
Also: curves from scalars, curves from curves, multiple regression.
Administrivia Introduction Outline
Relationships Between Derivatives
Administrivia Introduction Outline
Course Outline
Introduction: Matlab, FDA Toolbox, Vizualisation, ProjectsSmoothing: Series estimators, splines, kernel estimates,
computationFunctional Data Analysis: Functional analysis, modes of variation,
functional linear modelsAnalysis of Derivatives: Differential equations, principle differential
analysis, interpretationConstrained Smoothing: Positive, monotone smoothing; density
estimation, registration.Requests and Suggestions
