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
Unit Level Model
5
n informatioAuxiliary
discrete and Continuous
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Parameters
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9
Double Bootstrap Estimation
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10
Fast Double Bootstrap
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12
CEAP Simulation Model
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13
Alternative Specifications for x
Some external information
Area means known
Estimated random means
No external information
Area means fixed
Area means random
14
Simulation Parameters
)36.0,16.0,25.0(),,(
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each 12)40,10,2( areas; 36
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16
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
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~ No
Fixed
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Random
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Random
17
)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
18
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
19
Future Work
Confidence Intervals
Triple Bootstrap
Regression with Bootstrap
Nonparametric Bootstrap
Predictions for CEAP
20