Reminiscences, and some explorations about the bootstrap

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.