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arXiv · 2409.16409

Mean Squared Prediction Error Estimators of EBLUP of a Small Area Mean Under a Semi-Parametric Fay-Herriot Model

Shijie Chen·P. Lahiri·J. N. K. Rao
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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. It is interesting to note that 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.

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Shijie Chen, P. Lahiri, J. N. K. Rao. 2024-09-24. Mean Squared Prediction Error Estimators of EBLUP of a Small Area Mean Under a Semi-Parametric Fay-Herriot Model. https://arxiv.org/abs/2409.16409

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