Discussion

Abstract

This is a discussion of the Forum Lectures by Evarist Ginéon the subject of Empirical Processes and Applications presented at the European Meeting of Statisticians held in Bath, England, September 13-18, 1992. The discussion includes short sketches of developments in probability theory (Gaussian process theory, weak convergence theory, and probability in Banach spaces), empirical process theory, and applications thereof in statistics. I comment briefly on the formulation of central limit theorems for empirical processes in terms of the presence or absence of a Gaussian hypothesis, expand on Professor Giné's discussion of the bootstrap, and briefly explain my recent results for exchangeably weighted bootstraps obtained jointly with Jens Praestgaard. The discussion closes with some problems.