On the performance of self benchmarked small area estimators under the Fay-Herriot area level model

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Yong You, J.N.K. Rao and Mike Hidiroglou1


We consider two different self-benchmarking methods for the estimation of small area means based on the Fay-Herriot (FH) area level model: the method of You and Rao (2002) applied to the FH model and the method of Wang, Fuller and Qu (2008) based on augmented models. We derive an estimator of the mean squared prediction error (MSPE) of the You-Rao (YR) estimator of a small area mean that, under the true model, is correct to second-order terms. We report the results of a simulation study on the relative bias of the MSPE estimator of the YR estimator and the MSPE estimator of the Wang, Fuller and Qu (WFQ) estimator obtained under an augmented model. We also study the MSPE and the estimators of MSPE for the YR and WFQ estimators obtained under a misspecified model.

Key Words

Augmented model; Empirical best linear unbiased prediction; Mean squared prediction error; Model misspecification.

Table of content

1 Introduction

2 EBLUPs and WFQ estimators

3 YR estimator

4 Simulation study

5 Concluding remarks






1  Yong You, Statistical Research and Innovation Division, Statistics Canada, Ottawa, Canada. E-mail: yong.you@statcan.gc.ca; J.N.K. Rao, School of Mathematics and Statistics, Carleton University, Ottawa, Canada; Mike Hidiroglou, Statistical Research and Innovation Division, Statistics Canada, Ottawa, Canada.

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