Development of robust Bayes estimators for a multivariate normal mean
Abstract
Estimation of the mean of a multivariate normal distribution is considered. The goal is to develop robust Bayes estimators for the mean, estimators which are insensitive to partial misspecification of the prior information. These estimators will be developed using hierarchical Bayesian methodology. Two cases will be considered. In the first, the components of the mean vector, $\theta$, are assumed to be exchangeable with a Cauchy distribution as the first stage prior. In this situation, the estimator will be robust with respect to outliers. In the second case, $\theta$ is assumed to arise from a mixed model, where exchangeability within each random effect vector is assumed. A robust estimator, with respect to misspecification of the location information, will be developed by taking a multivariate t-distribution as the first stage prior on the fixed effect vector.
Degree
Ph.D.
Advisors
Berger, Purdue University.
Subject Area
Statistics
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