Survey Methodology
Mean squared prediction error estimators of the empirical best linear unbiased predictor of a small area mean under a semi-parametric Fay-Herriot model

by Shijie Chen, Partha Lahiri and J.N.K. RaoNote 1

  • Release date: June 30, 2025
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Abstract

In this paper, we derive a second-order unbiased (or nearly unbiased) mean squared prediction error (MSPE) estimator of the empirical best linear unbiased predictor (EBLUP) of a small area mean for a semi-parametric extension to the well-known Fay-Herriot model. Specifically, we derive our MSPE estimator essentially assuming certain moment conditions on both the sampling errors and random effects distributions. The normality-based Prasad-Rao MSPE estimator has a surprising robustness property in that it remains second-order unbiased under the non-normality of random effects when a simple Prasad-Rao method-of-moments estimator is used for the variance component and the sampling error distribution is normal. We show that the normality-based MSPE estimator is no longer second-order unbiased when the sampling error distribution has non-zero kurtosis or when the Fay-Herriot moment method is used to estimate the variance component, even when the sampling error distribution is normal. Interestingly, when the simple method-of moments estimator is used for the variance component, our proposed MSPE estimator does not require the estimation of kurtosis of the random effects. Results of a simulation study on the accuracy of the proposed MSPE estimator, under non-normality of both sampling and random effects distributions, are also presented.

Key Words:    Linear mixed model; Mean squared prediction errors; Variance components.

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How to cite

Chen, S., Lahiri, P. and Rao, J.N.K. (2025). Mean squared prediction error estimators of the empirical best linear unbiased predictor of a small area mean under a semi-parametric Fay-Herriot model. Survey Methodology, 51(1), 233-250. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2025001/article/00005-eng.pdf.

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ISSN : 1492-0921

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Published by authority of the Minister responsible for Statistics Canada.

© His Majesty the King in Right of Canada, as represented by the Minister of Industry, 2025

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Catalogue No. 12-001-X

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