Yale University
Department of Statistics

Monday, February 19, 1996

Guenther Walther
Department of Statistics
Stanford University

"Granulometric Smoothing"

A method for `smoothing' a multivariate data set is introduced that is based on a simple geometric idea. This method is applied to the problem of estimating level sets of a density and minimum volume sets with given probability content, with the goal of constructing certain multivariate bootstrap confidence regions and highest posterior density regions in a Bayesian context. Building on existing techniques, the resulting estimator combines excellent theoretical and computational properties for a very flexible class of sets: It converges with the minimax rates (up to log factors) in most cases where these rates are known and allows at the same time to be computed, visualized, stored and manipulated by simple algorithms and tools.

Seminar to be held in Room 107, 24 Hillhouse Ave at 4:15 pm