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Statistics Colloquium/Ph.D. Defense
March 18 (Friday) 11 a.m. noon
6625 Everett Tower
James Dzikunu
Department of Statistics
Western Michigan University
A Bayesian Rank Based Method for linear models is developed in this research. The estimation of the regression coefficients is based on the full conditional distributions utilizing a rank-based initial fit. The data likelihood is based on the asymptotic distribution of the gradient function and the asymptotic linearity of this rank-based procedure. Prior distributions are put on regression coefficients and scale parameters. The effects of different priors on this scale parameters are studied. Using these full conditional distributions, the estimates are obtained by a Markov Chain Monte-Carlo (MCMC) procedure. The results of our simulation studies show that these Bayesian rank-based estimates retain the robustness of the rank-based fit. In many of the situations they were more efficacious than the rank-based fits. For error distributions with heavy tails, they were much more efficient than traditional least squares estimates. These investigations also showed that incorporating prior information on the scale parameter resulted in much more efficient estimates over all situations investigated.
Although robust in the response space, similar with the rank-based initial fit, our procedure is not robust in factor space. To counter this, we also developed a Bayesian High Breakdown rank-based estimate which is robust in both the response and factor spaces.
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All statistics students are expected to attend.