Robust linear mixed models for Small Area Estimation

Hierarchical models are popular in many applied statistics fields including Small Area Estimation. One well known model employed in this particular field is the Fay–Herriot model, in which unobservable parameters are assumed to be Gaussian. In Hierarchical models assumptions about unobservable quant...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2010-02, Vol.140 (2), p.433-443
Main Authors: Fabrizi, Enrico, Trivisano, Carlo
Format: Article
Language:English
Subjects:
Applications
Distribution theory
Exact sciences and technology
Exponential power distribution
Fay–Herriot model
General topics
Insurance, economics, finance
Mathematics
Nonparametric inference
Probability and statistics
Sciences and techniques of general use
Skewed exponential power distribution
Statistics
‘Ensemble’ estimators
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Summary:Hierarchical models are popular in many applied statistics fields including Small Area Estimation. One well known model employed in this particular field is the Fay–Herriot model, in which unobservable parameters are assumed to be Gaussian. In Hierarchical models assumptions about unobservable quantities are difficult to check. For a special case of the Fay–Herriot model, Sinharay and Stern [2003. Posterior predictive model checking in Hierarchical models. J. Statist. Plann. Inference 111, 209–221] showed that violations of the assumptions about the random effects are difficult to detect using posterior predictive checks. In this present paper we consider two extensions of the Fay–Herriot model in which the random effects are assumed to be distributed according to either an exponential power (EP) distribution or a skewed EP distribution. We aim to explore the robustness of the Fay–Herriot model for the estimation of individual area means as well as the empirical distribution function of their ‘ensemble’. Our findings, which are based on a simulation experiment, are largely consistent with those of Sinharay and Stern as far as the efficient estimation of individual small area parameters is concerned. However, when estimating the empirical distribution function of the ‘ensemble’ of small area parameters, results are more sensitive to the failure of distributional assumptions.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2009.07.022