JSM 2004 - Toronto

Abstract #300068

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Activity Number: 286
Type: Invited
Date/Time: Wednesday, August 11, 2004 : 8:30 AM to 10:20 AM
Sponsor: Section on Survey Research Methods
Abstract - #300068
Title: Estimation of a Finite Population Mean--an Empirical Restricted Best Prediction Approach
Author(s): Jiming Jiang*+ and Partha Lahiri
Companies: University of California, Davis and University of Maryland
Address: Dept. of Statistics, Davis, CA, 95616,
Keywords: design consistency ; empirical restricted best predictor ; finite population mean ; mean squared prediction error ; small-area estimation
Abstract:

We propose a model-based restricted best (RB) predictor of a finite population mean that minimizes the mean square prediction error (MSPE) among the class of all predictors that depend on the sample only through the traditional design-unbiased estimator of the finite population mean. We then consider an empirical restricted best (ERB) predictor derived from the RB that does not require the knowledge of an explicit model for the unobserved units of the finite population. The proposed ERB enjoys a robust design-consistency property irrespective of the assumed model, and it applies to a wide class of models, including linear and generalized linear mixed models. The case of unknown model parameters is undertaken and a second-order accurate model-based MSPE of the proposed ERB predictor is obtained to measure the precision of the proposed predictor. The method will find applications in small-area estimation.

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