Degree Type

Dissertation

Date of Award

1983

Degree Name

Doctor of Philosophy

Department

Statistics

Abstract

A prediction approach to small area estimation is presented. The procedure uses survey and auxiliary data and is based on the assumption of a nested-error model. The mean squared error and the mean squared conditional bias of the predictor are given. Under the nested-error model, the best linear unbiased predictor of the small area mean has the form of a James-Stein estimator;Estimators for the variance components of the nested-error model are suggested. A generalized least squares procedure is given for constructing estimators of the variance components given prior estimators of the components. The asymptotic distribution of the estimated generalized least squares estimator of the fixed effects is presented and the approximate mean squared error of the predictor is derived;The Statistical Reporting Service of the U.S. Department of Agriculture (USDA) collects data on hectares of crops in the June Enumerative Survey. Auxiliary data from LANDSAT satellites is available for the same areas. The prediction procedure for the homogeneous nested-error model is illustrated by using the USDA and LANDSAT data to predict corn and soybean hectares for 12 Iowa counties. The prediction procedure for the heterogeneous nested-error model is illustrated by estimating the percentage of urban acres in five Alabama counties.

DOI

https://doi.org/10.31274/rtd-180813-8573

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Rachel Margaret Harter

Language

en

Proquest ID

AAI8407074

File Format

application/pdf

File Size

256 pages

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