small area prediction under alternative model specifications by wayne a. fuller and andreea l....
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Small Area Prediction under Alternative Model Specifications
By
Wayne A. Fuller and Andreea L. Erciulescu
Department of Statistics, Iowa State University
Small Area Estimation 2014
Poznan, Poland, September, 2014
2
Outline
I. Motivating example
II. Models: auxiliary information
III. Bootstrap for prediction MSE
IV. Simulation
Conservation Effects Assessment Project (CEAP): Natural Resources Conservation Service
Impacts of conservation practices
Sample of fields
Subsample: National Resources Inventory(NRI)
Hydrologic Units
3
4
Unit Level Model
5
n informatioAuxiliary
discrete and Continuous
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Auxiliary Data
6
(NRI) practices Cover, :~(known) data Soils :
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Parameters
7
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Double Bootstrap Estimation
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Fast Double Bootstrap
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Telescoping Double Bootstrap
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CEAP Simulation Model
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Alternative Specifications for x
Some external information
Area means known
Estimated random means
No external information
Area means fixed
Area means random
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Simulation Parameters
)36.0,16.0,25.0(),,(
)0.1,8.0,0.0(),,(
)exp(1
)exp(),(
),(}|{ bernoulli
each 12)40,10,2( areas; 36
222
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Estimation and Prediction
}ˆ),~,,(|{ˆ
),,( and ),(for REML 222
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KnownMSE tionMSE/PredicPrediction xiμ
Size
2 1.76 1.43 1.16
10 1.20 1.12 1.05
40 1.09 1.04 1.02
xi
xi
~ No
Fixed
xi
xi
~ No
Random
xi
xi
~
Random
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)1,100(),( Samples, 400 21 BBMC
(%), MSE Prediction ofEstimator Bootstrap
2 Rel Bias -14.6 -9.4 -9.4
Rel Sd 38.9 45.1 44.7
10 Rel Bias -13.2 -6.8 -6.8
Rel Sd 30.7 36.5 35.9
40 Rel Bias -7.5 -1.9 -1.9
Rel Sd 20.1 23.3 25.1
***** ˆˆˆ Size CT xixi ~ Observed , Random
Equal Efficiency Bootstrap Samples
Random , Observed
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Bootstrap Level One TotalTelescoping (100, 1) 100 200Classic (100, 1) 150 300Classic (44, 50) 44
2244
Summary
Fast double bootstrap improves bootstrap efficiency
Double bootstrap reduces bias (about 50%)
Double bootstrap increases variance (15 to 30 %)
Random x model has potential to reduce MSE
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Future Work
Confidence Intervals
Triple Bootstrap
Regression with Bootstrap
Nonparametric Bootstrap
Predictions for CEAP
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Thank You
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