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SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
Estimation of Complex Small AreaParameters with Application to Poverty
Indicators
J.N.K. RaoSchool of Mathematics and Statistics, Carleton University
(Joint work with Isabel Molina from Universidad Carlos III de Madrid)
JPSM-Census Distinguished Lecture
September 30, 2011
1
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
2
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
SAE
POVERTY INDICATORS
EB
ELL
SIMULATIONS
MODIFICATIONS
EXTENSIONS
CONCLUSIONS
3
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
NOTATION
• U finite population of size N.
• Population partitioned into D subsets U1, . . . ,UD of sizesN1, . . . ,ND , called domains or areas.
• Variable of interest Y .
• Ydj value of Y for unit j from domain d .
• Target: to estimate domain parameters.
δd = h(Yd1, . . . ,YdNd), d = 1, . . . ,D.
• We want to use data from a sample S ⊂ U of size n drawnfrom the whole population.
• Sd = S ∩ Ud sub-sample from domain d of size nd .
• Problem: nd small for some domains.
4
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
DIRECT ESTIMATORS
• Direct estimator: Estimator that uses only the sample datafrom the corresponding domain.
• Small area/domain: subset of the population that is targetof inference and for which the direct estimator does not haveenough precision.
• What does “enough precision” mean? Some NationalStatistical Offices (GB, Spain) allow a maximum coefficient ofvariation of 20 %.
• Indirect estimator: Borrows strength from other areas.
5
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
NESTED-ERROR REGRESSION MODEL
• Model: xdj auxiliary variables at unit level,
Ydj = x′djβ + ud + edj , udiid∼ N(0, σ2u), edj
iid∼ N(0, σ2e ).
• Vector of variance components:
θ = (σ2u, σ2e )′
• BLUP of small area mean Yd :
Predict non-sample values Ydj(θ) = x′dj βWLS + ud(θ).
ˆY BLUPd (θ) =
1
Nd
∑j∈sd
Ydj +∑j∈rd
Ydj(θ)
, d = 1, . . . ,D.
6
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
NESTED-ERROR REGRESSION MODEL
• BLUP of small area mean Yd :
ˆY BLUPd (θ) ≈ γd{yd + (Xd − xd)′βWLS︸ ︷︷ ︸
sample regression est.
}+ (1− γd)x′βWLS︸ ︷︷ ︸synthetic est.
,
γd = σ2u/(σ2u + σ2e/nd).
• Note: BLUP does not require normality.
• Empirical BLUP (EBLUP): θ estimator of θ
ˆY EBLUPd = ˆY BLUP
d (θ)
• EBLUP is identical to EB under normality.
X Battese, Harter & Fuller (1988), JASA 7
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
SOME POVERTY AND INCOME INEQUALITYMEASURES
• FGT poverty indicator
• Gini coefficient
• Sen index
• Theil index
• Generalized entropy
• Fuzzy monetary index
8
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
FGT POVERTY INDICATORS
• Edj welfare measure for indiv. j in domain d : for instance,equivalised annual net income.
• z = poverty line.
• FGT family of poverty indicators for domain d :
Fαd =1
Nd
Nd∑j=1
(z − Edj
z
)αI (Edj < z), α = 0, 1, 2.
When α = 0⇒ Poverty incidence
When α = 1⇒ Poverty gap
When α = 2⇒ Poverty severity
X Foster, Greer & Thornbecke (1984), Econometrica 9
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
COMPUTATIONALLY COMPLEX POVERTYINDICATORS
• Fuzzy Monetary Index (FMI): It is based on degree of povertyof each individual relative to other individuals in thepopulation.
• Let
Ai =
∑j 6=i I (Ej > Ei )
N − 1, Bi =
∑j 6=i Ej I (Ej > Ei )∑
j Ej
• Ai = Proportion of individuals less poor than individual i• Bi = Share of total welfare of all individuals less poor than i• FMi = Aα−1i Bi , α > 1.• Then FMI for domain d is
FMd =1
Nd
Nd∑j=1
FMdj .
10
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
FGT POVERTY INDICATORS
• Complex non-linear quantities (non continuous): Even ifFGT poverty indicators are also means
Fαd =1
Nd
Nd∑j=1
Fαdj , Fαdj =
(z − Edj
z
)αI (Edj < z),
we cannot assume normality for the Fαdj .
• Not easy to obtain small area estimators with good bias andMSE properties.
• A method valid to estimate poverty measures in small areasfor any α and for other poverty or inequality measures wouldbe desirable.
11
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
SMALL AREA ESTIMATION
• Due to the relative nature of the mentioned poverty line,poverty has usually low frequency: Large sample size isneeded.
X In Spain, poverty line for 2006: 6557 euros, approx. 20 %population under the line.
• Survey on Income and Living Conditions (EU-SILC) haslimited sample size.
X In the Spanish SILC 2006, n = 34,389 out ofN = 43,162,384 (8 out 10,000).
12
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
SAMPLE SIZES OF PROVINCES BY GENDER
• Direct estimators for Spanish provinces are not very precise.
• Provinces × Gender → Small areas (52 × 2).
• CVs of direct and EB estimators of poverty incidences for 5selected provinces:
Province Gender nd Obs. Poor CV Dir. CV EB
Soria F 17 6 40.37 16.52Tarragona M 129 18 19.85 16.15Cordoba F 230 73 7.52 6.73Badajoz M 472 175 7.12 3.57
Barcelona F 1483 191 6.67 5.37
13
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
EB METHOD (EMPIRICAL BEST/BAYES)
• Vector with population elements for domain d :
yd = (Yd1, . . . ,YdNd)′ = (y′ds , y
′dr )′
• Target parameter:δd = h(yd)
• Best estimator: The estimator δd that minimizes the MSE is
δBd = Eydr (δd |yds).
• Best estimator of Fαd : We need to express δd = Fαd interms of a vector yd = (y′ds , y
′dr )′,
Fαd = hα(yd)
for which we can derive the distribution of ydr |yds .
14
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
EB METHOD FOR POVERTY ESTIMATION
• Assumption: there exists a transformation Ydj = T (Edj) ofthe welfare variables Edj which follows a normal distribution(i.e., the nested error model with normal errors ud and edj).
• FGT poverty indicator as a function of transformed variables:
Fαd =1
Nd
Nd∑j=1
{z − T−1(Ydj)
z
}αI{T−1(Ydj) < z
}.
• EB estimator of Fαd :
FEBαd = Eydr [Fαd |yds ] , Fαd = hα(yd).
15
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
EB METHOD FOR POVERTY ESTIMATION
• Distribution: ydind∼ N(µd ,Vd), d = 1 . . . ,D, where
yd =
(ydsydr
), µd =
(µds
µdr
), Vd =
(Vds Vdsr
Vdsr Vdr
).
• Distribution of ydr given yds :
ydr |yds ∼ N(µdr |ds ,Vdr |ds),
where
µdr |ds = µdr + VdrsV−1ds (yds − µds),
Vdr |ds = Vdr − VdrsV−1ds Vdsr .
16
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
EB METHOD FOR POVERTY ESTIMATION
• For the nested-error model:
µdr |ds = Xdrβ + σ2u1Nd−nd 1′nd V−1ds (yds − Xdsβ)
Vdr |ds = σ2u(1− γd)1Nd−nd 1′Nd−nd + σ2e INd−nd ,
whereγd = σ2u(σ2u + σ2e/nd)−1
• Model for simulations:
ydr = µdr |ds + vd1Nd−nd + εdr ,
with
vd ∼ N{0, σ2u(1− γd)} and εdr ∼ N(0Nd−nd , σ2e INd−nd ).
• We only need to generate N + D univariate normal randomvariables.
X Molina and Rao (2010), CJS 17
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
MONTE CARLO APPROXIMATION
(a) Generate L non-sample vectors y(`)dr , ` = 1, . . . , L from the
(estimated) conditional distribution of ydr |yds .
(b) Attach the sample elements to form a population vector
y(`)d = (yds , y
(`)dr ), ` = 1, . . . , L.
(c) Calculate the poverty measure with each population vector
F(`)αd = hα(y
(`)d ), ` = 1, . . . , L. Then take the average over the
L Monte Carlo generations:
FEBαd = Eydr [Fαd |yds ] ∼=
1
L
L∑`=1
F(`)αd .
18
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
NON-SAMPLED AREAS
• Y(`)dj for j = 1, . . . ,Nd and ` = 1, . . . , L generated from
Y(`)dj = x′dj β + u
(`)d + e
(`)dj .
u(`)d
iid∼ N(0, σ2u); e(`)dj
iid∼ N(0, σ2e ).
• Calculate F(`)αd from {Y (`)
dj } and use
FEBαd '
1
L
L∑`=1
F(`)αd
• FEBαd is a synthetic estimator.
19
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
MSE ESTIMATION
• Construct bootstrap populations {Y ∗(b)dj , b = 1, . . . ,B} from
Y ∗dj = x′dj β + u∗d + e∗dj ; j = 1, . . . ,Nd , d = 1, . . . ,D.
u∗diid∼ N(0, σ2u); e∗dj
iid∼ N(0, σ2e ).
• Calculate bootstrap population parameters F ∗αd(b)
• From each bootstrap population, take the sample with thesame indexes S as in the initial sample and calculate EBsFEB∗αd (b) using bootstrap sample data y∗s and known xdj .
mse∗(FEBαd ) =
1
B
B∑b=1
{FEB∗αd (b)− F ∗αd(b)}2
20
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
WORLD BANK (WB) / ELL METHOD
• Elbers et al. (2003) also used nested error model ontransformed variables Ydj , using clusters as d .
• For comparability we take cluster as small area.
• Generate A bootstrap populations {Y ∗dj(a), a = 1, . . . ,A}
• Calculate F ∗αd(a), a = 1, . . . ,A. Then ELL estimator is:
F(ELL)αd =
1
A
A∑a=1
F ∗αd(a) = F ∗αd(·)
21
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
WORLD BANK (WB) / ELL METHOD
• MSE estimator:
mse(FELLαd ) =
1
A
A∑a=1
{F ∗αd(a)− F ∗αd(·)}2
• If the mean Yd is the parameter of interest, then
ˆY(ELL)d ' Xd β
• ˆY(ELL)d is a regression synthetic estimator.
• For non-sampled areas, FELLαd is essentially equivalent to FEB
αd .
• But MSE estimators are different for ELL and EB.
22
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
MODEL-BASED EXPERIMENT
• We simulated I = 1000 populations from the nested errormodel;
• For each population, we computed the true domain povertymeasures.
• We computed the MSE of the EB estimators as
MSE(FEBαd ) =
1
I
I∑i=1
(FEB(i)αd − F
(i)αd
)2, d = 1, . . . ,D.
• Similarly for direct and ELL estimators.
23
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
MODEL-BASED EXPERIMENT
Sizes:
N = 20000D = 80Nd = 250, d = 1, . . . ,Dnd = 50, d = 1, . . . ,D
Variance components:
σ2e = (0,5)2
σ2u = (0,15)2 24
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
MODEL-BASED EXPERIMENT
Explanatory variables:
X1 ∈ {0, 1}, p1d = 0.3 + 0.5d/80, d = 1, . . . ,D.
X2 ∈ {0, 1}, p2d = 0.2, d = 1, . . . ,D.
Coefficients:β = (3, 0.03,−0.04)′.
• The response increases when moving from X1 = 0 to X1 = 1,and decreases when moving from X2 = 0 to X2 = 1.
• The “richest” people are those with X1 = 1 and X2 = 0.
• The last areas have “richer” individuals than the first areas,i.e., poverty decreases with the area index.
25
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
POVERTY INCIDENCE• Bias negligible for all three estimators (EB, direct and ELL).• EB much more efficient than ELL and direct estimators.• ELL even less efficient than direct estimators!
a) Bias ( %)
0 20 40 60 80
−0.
3−
0.2
−0.
10.
00.
10.
20.
3
Area
Bia
s po
vert
y in
cide
nce
(x10
0)
EB Sample ELL
b) MSE (×104)
0 20 40 60 80
1020
3040
5060
70
Area
MS
E p
over
ty in
cide
nce
(x10
000)
EB Sample ELL
Figure 1. a) Bias and b) MSE of EB, direct and ELL estimators of
poverty incidences F0d for each area d . 26
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
POVERTY GAP
• Same conclusions as for poverty incidence.
a) Bias ( %)
0 20 40 60 80
−0.
10−
0.05
0.00
0.05
0.10
Area
Bia
s po
vert
y ga
p (x
100)
EB Direct ELL
b) MSE (×104)
0 20 40 60 80
12
34
Area
MS
E p
over
ty g
ap (
x100
00)
EBDirectELL
Figure 2. a) Bias and b) MSE of EB, direct and ELL estimators of
poverty gaps F1d for each area d . 27
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
BOOTSTRAP MSE
• The bootstrap MSE tracks true MSE.
a) MSE of poverty incidence
0 20 40 60 80
10.0
10.2
10.4
10.6
10.8
Area
MS
E P
over
ty in
cide
nce
(x10
000)
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b) MSE of poverty gap
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0.86
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MS
E P
over
ty g
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00)
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Figure 3. True MSEs and bootstrap estimators (×104) of EB estimators
with B = 500 for each area d . 28
0 20 40 60 80
12.4
12.6
12.8
13.0
13.2
13.4
13.6
Area
MS
E E
LL e
stim
ator
of m
eans
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SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
CENSUS EB METHOD• When sample data cannot be linked with census auxiliary data,in steps (a) and (b) of EB method generate a full census from
yd = µd |ds+vd1Nd+εd , µd |ds = Xd β+σ2u1Nd
1′nd V−1ds (yds−Xds β).
• Practically the same as original EB method.
a) Mean (×100)
0 20 40 60 80
3.3
3.4
3.5
3.6
3.7
3.8
Area
Pov
erty
inci
denc
e (x
100)
EB Census EB
b) MSE (×104)
0 20 40 60 80
9.5
10.0
10.5
11.0
11.5
12.0
Area
MS
E p
over
ty in
cide
nce
(x10
000)
EB Census EB
Figure 4. a) Mean and b) MSE of EB and Census EB estimators of
poverty gaps F1d for each area d . 29
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
FAST EB METHOD• For large populations or computationally complex indicators.• Instead of generating a full census in the EB method, generateonly samples from the conditional distribution and compute directestimators instead of true values.• Fast EB method quite close to original EB.
0 20 40 60 80
01
23
45
67
Area
MSE
PI (x
1000
)
EBDesign−basedELLfastEB
Figure 5. MSE (×104) of EB, direct, ELL and fast EB estimators of PI.
X Ferretti, Molina & Lemmi, Submitted to JISAS 30
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
SKEW-NORMAL EB
• Nester error model with edj skew normal
udiid∼ N(0, σ2u), edj
iid∼ SN(0, σ2e , λe)
θ = (β′, σ2u, σ2e , λe)′
λe = 0 corresponds to Normal
• As in the Normal case, EB estimator can be computed bygenerating only univariate normal variables, conditionallygiven a half-normal variable T = t.
• SN-EB was computed assuming θ is known.
31
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
SKEW-NORMAL EB SIMULATION
• EB biased under significant skewness (λ > 1) unlike SN EB.
a) Bias of SN-EB estimator
0 20 40 60 80
0.0
0.2
0.4
0.6
0.8
1.0
Area
Bia
s:
Po
ve
rty G
ap
(x1
00
)
SN(0.5,10) SN(0.5,5) SN(0.5,3) SN(0.5,2) SN(0.5,1)
b) Bias of EB estimator
0 20 40 60 80
0.0
0.2
0.4
0.6
0.8
1.0
Area
Bia
s:
Po
ve
rty G
ap
(x1
00
)
SN(0.5,10) SN(0.5,5) SN(0.5,3) SN(0.5,2) SN(0.5,1)
Figure 6. Bias of a) SN-EB estimator and b) EB estimator under skew
normal distributions for error term for λ = 1, 2, 3, 5, 10.
X Diallo & Rao, Work in progress 32
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
SKEW-NORMAL EB SIMULATION
• RMSE = MSE(EB)/MSE(SN-EB)
• SN-EB significantly more efficient than EB when λ > 1.
0 20 40 60 80
1.0
1.5
2.0
2.5
Area
RM
SE
= M
SE
(MR
)/M
SE
(SN
-MR
): P
ove
rty G
ap SN(0.5,10) SN(0.5,5) SN(0.5,3) SN(0.5,2) SN(0.5,1) SN(0.5,0)
Figure 7. RMSE for skewness parameter λ = 1, 2, 3, 5, 10. 33
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
SMALL AREA DISTRIBUTION FUNCTION• EB good for estimating other non-linear characteristics such asdistrib. function.
a) Mean (×100)
0 10 20 30 40
0.0
0.2
0.4
0.6
0.8
1.0
z
Dis
trib
. fun
ctio
n
● ●
●
●
●
●
●
●
●
●
●●
●
EBDirectELL
b) MSE (×104)
0 10 20 30 40
050
100
150
z
MS
E D
istr
ib. F
unct
ion
EBDirectELL
Figure 8. a) Mean of true, EB, direct and ELL estimators of the
distribution function and b) MSE of estimators for area d = 1. 34
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
HIERARCHICAL BAYES METHOD• Reparameterized nested-error model:
ydi |ud ,β, σ2ind∼ N(x′diβ + ud , σ
2)
ud |ρ, σ2ind∼ N
(0,
ρ
1− ρσ2)
• Noninformative prior: π(β, σ2, ρ) ∝ 1/σ2.
• Proper posterior density (provided X full column rank):
π(u,β, σ2, ρ|ys) = π1(u|β, σ2, ρ, ys)π2(β|σ2, ρ, ys)π3(σ2|ρ, ys)π4(ρ|ys)
• ui |β, σ2, ρ, ys ∼ind Normal , β|σ2, ρ, ys ∼ Normal ,σ−2|ρ, ys ∼ Gamma.
• π4(ρ|ys) is not simple but ρ-values from it can be generatedusing a grid method.
X Rao, Nandram & Molina, Work in progress 35
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
HIERARCHICAL BAYES METHOD• Very similar to original EB method (frequencial validity).
a) Mean (×100)
0 20 40 60 80
3.3
3.4
3.5
3.6
3.7
3.8
3.9
Area
Pov
erty
inci
denc
e (x
100)
EB HB
b) MSE (×104)
0 20 40 60 80
910
1112
13
Area
MS
E p
over
ty in
cide
nce
(x10
000)
EB HB
Figure 9. a) Mean and b) MSE of EB and HB estimators of poverty
gaps F1d for each area d .
X Rao, Nandram & Molina, Work in progress 36
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
M-QUANTILE (MQ) METHOD• MQ estimator of Fαd :
Fαd =1
Nd
∑j∈sd
Fαdj +∑k∈rd
FMQαdk
FMQαdk =
1
nd
∑j∈sd
(z − EMQ
dk
z
)αI[EMQdk + (Edj − EMQ
dj ) < z]
EMQdk = MQ predictor of Edk
• Normality not needed• Robust to outliers• Nested error model not used but poor efficiency if area sample
size is small and nested error model with strong area effectsholds.
• It is not clear how MQ can be applied to FMI and othercomplex poverty indicators
37
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
CONCLUSIONS
• We studied EB and HB estimation of complex small areaparameters.
• Method applicable to unit level data.
• EB method assumes normality for some transformation of thevariable of interest. EB work extended to skew normaldistributions.
• It requires the knowledge of all population values of theauxiliary variables.
• It requires computational effort because large number ofpopulations are generated. Fast EB method available.
38
SAE POVERTY INDICATORS EB ELL SIMULATIONS MODIFICATIONS EXTENSIONS CONCLUSIONS
CONCLUSIONS
• Original EB method, unlike ELL method, requires linkingsample with census data for the auxiliary variables. CensusEB method avoids the linking and is practically the same asoriginal EB.
• Both EB and ELL methods assume that the sample isnon-informative, that is, the model for the population holdsgood for the sample. Under informative sampling, probablyboth methods are biased. Currently an extension of EBmethod accounting for informative sampling is being studied.
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0 20 40 60 80
12.4
12.6
12.8
13.0
13.2
13.4
13.6
Area
MS
E E
LL e
stim
ator
of m
eans
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● True MSEBootstrap MSEELL MSE
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