Mean Squared Prediction Error Estimators of EBLUP of a Small Area Mean Under a Semi-Parametric Fay-Herriot Model
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| author | Chen, Shijie Lahiri, P. Rao, J. N. K. |
| author_facet | Chen, Shijie Lahiri, P. Rao, J. N. K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16409 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mean Squared Prediction Error Estimators of EBLUP of a Small Area Mean Under a Semi-Parametric Fay-Herriot Model Chen, Shijie Lahiri, P. Rao, J. N. K. Methodology 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. |
| title | Mean Squared Prediction Error Estimators of EBLUP of a Small Area Mean Under a Semi-Parametric Fay-Herriot Model |
| topic | Methodology |
| url | https://arxiv.org/abs/2409.16409 |