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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

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

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Conservation Effects Assessment Project (CEAP): Natural Resources Conservation Service Impacts of conservation practices Sample of fields Subsample: National Resources Inventory(NRI) Hydrologic Units 3

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Unit Level Model 5

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Auxiliary Data 6

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Parameters 7

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Parametric Bootstrap 8

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Double Bootstrap Estimation 9

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Fast Double Bootstrap 10

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Telescoping Double Bootstrap 11

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CEAP Simulation Model 12

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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 13

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Simulation Parameters 14

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Estimation and Prediction 15

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16 Size 21.761.431.16 101.201.121.05 401.091.041.02

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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

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

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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

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Future Work Confidence Intervals Triple Bootstrap Regression with Bootstrap Nonparametric Bootstrap Predictions for CEAP 20

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Thank You 21

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