A two component normal mixture alternative to the Fay-Herriot model

Adrijo  Chakraborty; Gauri  Sankar Datta; Abhyuday  Mandal

doi:https://doi.org/10.59170/stattrans-2016-004

A two component normal mixture alternative to the Fay-Herriot model

Adrijo Chakraborty NORC at the University of Chicago, Bethesda, MD 20814. , Gauri Sankar Datta Department of Statistics, University of Georgia, Athens, GA 30602, USA. Center for Statistical Research and Methodology, US Census Bureau, Washington, D.C. 20233 Disclaimer: This report is released to inform interested parties of research and to encourage discussion on work in progress. The views expressed are those of the authors and not necessarily those of the US Census Burea , Abhyuday Mandal 5Department of Statistics, University of Georgia, Athens, GA 30602, USA. Statistics in Transition new series, vol. 17, 2016, 1, pages: 67-90 Published online: 1 March 2016 https://doi.org/10.59170/stattrans-2016-004

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ABSTRACT

This article considers a robust hierarchical Bayesian approach to deal with random effects of small area means when some of these effects assume extreme values, resulting in outliers. In the presence of outliers, the standard Fay-Herriot model, used for modeling area-level data, under normality assumptions of random effects may overestimate the random effects variance, thus providing less than ideal shrinkage towards the synthetic regression predictions and inhibiting the borrowing of information. Even a small number of substantive outliers of random effects results in a large estimate of the random effects variance in the Fay-Herriot model, thereby achieving little shrinkage to the synthetic part of the model or little reduction in the posterior variance associated with the regular Bayes estimator for any of the small areas. While the scale mixture of normal distributions with a known mixing distribution for the random effects has been found to be effective in the presence of outliers, the solution depends on the mixing distribution. As a possible alternative solution to the problem, a two-component normal mixture model has been proposed, based on non-informative priors on the model variance parameters, regression coefficients and the mixing probability. Data analysis and simulation studies based on real, simulated and synthetic data show an advantage of the proposed method over the standard Bayesian Fay-Herriot solution derived under normality of random effects

KEYWORDS

Hierarchical Bayes, heavy-tail distribution, non-informative priors, robustness to outliers; small area estimation.

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