Title
High Dimensional Predictive Densities
Speaker
Xinyi Xu, Department of Statistics, The Wharton School, University of Pennsylvania
Abstract
Commonly used statistical approaches to prediction provide a single number as a forecast of an unknown future quantity, sometimes attaching an error bound to convey the uncertainty of the prediction. A more comprehensive approach to prediction provides a complete predictive estimate that assigns probabilities to every possible outcome that may occur. Because they are more comprehensive, such descriptions of uncertainty lead to better decision making and sharper assessment of risks. In this talk, the problem of estimating the predictive density of a multivariate normal variable under Kullback-Leibler loss is considered. We show that there exist broad classes of formal Bayes rules, including Bayes rules under superharmonic priors, which dominate the best invariant minimax estimator for this problem. We also show that the class of generalized Bayes estimators is a complete class, and obtain sufficient conditions for the admissibility of formal Bayes rules. Fundamental similarities and differences with the parallel theory of estimating a multivariate normal mean under quadratic loss are described throughout.
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.
