Reminiscences, and some explorations about the bootstrap

Abstract

The paper is a potpourri of short sections. There will be some reminiscences about Evarist (from the early 1970s), then some on infinite-dimensional limit theorems from 1950 through 1990. A section reviews a case of slow convergence in the central limit theorem for empirical processes (Beck, 1985) and another the “fast” convergence of Komlós–Major–Tusnády. The paper does an experimental exploration of bootstrap confidence intervals for the mean (of Pareto distributions) and (as less commonly seen) for the variance, of normal and Pareto distributions.