Bayesian Robust Analysis for Non-Normal Data Based on a Perturbed-t Model

다국어 초록 (Multilingual Abstract)

The article develops a new class of distributions by introducing a non-negative perturbing function tot distribution having location and scaleparameters. The class is obtained by using transformations and condition-ing. The class strictly includest and skew-t distributions. It provides yetother models useful for selection modeling and robustness analysis. Analyticforms of the densities are obtained and distributional properties are studied.These developments are followed by an easy method for estimating the dis-tribution by using Markov chain Monte Carlo. It is shown that the methodis straightforward to specify distributionally and to implement computation-ally, with output readily adopted for constructing required criterion. Themethod is illustrated by using a simulation study.AMS 2000 subject classications.Primary 62H10; Secondary 62F15.Keywords.Perturbedt-distribution, non-normal data, Bayesian robust analysis.1. IntroductionSuppose that the model where a random variableZ is distributed with densityg(zj) and that it is desired to make inferences about;where is aq-dimensionalvector of unknown parameters. The usual statistical analysis assumes that a ran-dom sample Z1;:;Z n fromg(zj) can be observed. There are many situations,however, in which such a random sample might not be available, for instance, if itis too dicult or too costly to obtain. Then statistical models have to be devel-oped to incorporate the non-randomness or bias in the observations. Weighteddistributions (Rao, 1985) arise when the density of the potential observationz gets distorted so that it is multiplied by some non-negative weight functionReceived February 2006; accepted October 2006.yThis research was supported by the Korea Research Foundation Grant funded by the KoreanGovernment (MOEHRD) KRF-2005-041-C00089.

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