# Small Area Prediction under Alternative Model Specifications By Wayne A. Fuller and Andreea L. Erciulescu Department of Statistics, Iowa State University.

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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

Outline I.Motivating example II.Models: auxiliary information III.Bootstrap for prediction MSE IV.Simulation 2

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

Auxiliary Data 6

Parameters 7

Parametric Bootstrap 8

Double Bootstrap Estimation 9

Fast Double Bootstrap 10

Telescoping Double Bootstrap 11

CEAP Simulation Model 12

Alternative Specifications for x Some external information Area means known Estimated random means No external information Area means fixed Area means random 13

Simulation Parameters 14

Estimation and Prediction 15

16 Size 21.761.431.16 101.201.121.05 401.091.041.02

17 2Rel Bias-14.6-9.4 Rel Sd38.945.144.7 10Rel Bias-13.2-6.8 Rel Sd30.736.535.9 40Rel Bias-7.5-1.9 Rel Sd20.123.325.1

Equal Efficiency Bootstrap Samples 18 BootstrapLevel OneTotal Telescoping (100, 1) 100 200 Classic (100, 1) 150 300 Classic (44, 50) 442244

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

Thank You 21

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