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Reminiscences, and some explorations about the bootstrap. (English) Zbl 1387.60007

Summary: 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 [J. Beck, Z. Wahrscheinlichkeitstheor. Verw. Geb. 70, 289–306 (1985; Zbl 0554.60037)] 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.

MSC:

60-03 History of probability theory
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60F05 Central limit and other weak theorems
60F17 Functional limit theorems; invariance principles
62F40 Bootstrap, jackknife and other resampling methods

Citations:

Zbl 0554.60037
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Full Text: DOI

References:

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