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Über dieses Buch

This volume presents selections of Peter J. Bickel’s major papers, along with comments on their novelty and impact on the subsequent development of statistics as a discipline. Each of the eight parts concerns a particular area of research and provides new commentary by experts in the area. The parts range from Rank-Based Nonparametrics to Function Estimation and Bootstrap Resampling. Peter’s amazing career encompasses the majority of statistical developments in the last half-century or about about half of the entire history of the systematic development of statistics. This volume shares insights on these exciting statistical developments with future generations of statisticians. The compilation of supporting material about Peter’s life and work help readers understand the environment under which his research was conducted. The material will also inspire readers in their own research-based pursuits. This volume includes new photos of Peter Bickel, his biography, publication list, and a list of his students. These give the reader a more complete picture of Peter Bickel as a teacher, a friend, a colleague, and a family man.



Chapter 1. Rank-Based Nonparametrics

Peter Bickel has contributed substantially to the study of rank-based nonparametric statistics. Of his many contributions to research in this area I shall discuss his work on second order asymptotics that yielded surprising results and set off more than a decade of research that deepened our understanding of asymptotic statistics. I shall restrict my discussion to two papers, which are Albers et al. (1976) “Asymptotic expansions for the power of distribution free tests in the one-sample problem” and Bickel (1974) “Edgeworth expansions in nonparametric statistics” where the entire area is reviewed.

Willem R. van Zwet

Chapter 2. Robust Statistics

This is a short introduction to three papers on robustness, published by Peter Bickel as single author in the period 1975–1984: “One-step Huber estimates in the linear model” (Bickel 1975), “Parametric robustness: small biases can be worthwhile” (Bickel 1984a), and “Robust regression based on infinitesimal neighbourhoods” (Bickel1984b). It was the time when fundamental developments and understanding in robustness took place, and Peter Bickel has made deep contributions in this area. I am trying to place the results of the three papers in a new context of contemporary statistics.

Peter Bühlmann

Chapter 3. Asymptotic Theory

Asymptotic theory plays a fundamental role in the developments of modern statistics, especially in the theoretical analysis of new methodologies. Some asymptotic results may borrow directly from the limit theory in probability, but many need deep insights of statistical contents and more accurate approximations, which have in turn fostered further developments of limit theory in probability. Peter Bickel has made far-reaching and wide-ranging contributions to modern statistics. He is a giant in theoretical statistics. In asymptotic theory, besides his contributions to bootstrap and high-dimensional statistical inference, in this paper I shall focus on four of his seminal papers on asymptotic expansions and Bartlett correction for Bayes solutions, likelihood ratio statistics and maximum-likelihood estimator for general hidden Markov models. The papers will be reviewed in chronological order.

Qi-Man Shao

Chapter 4. Function Estimation

The following is a brief review of three landmark papers of Peter Bickel on theoretical and methodological aspects of nonparametric density and regression estimation and the related topic of goodness-of-fit testing, including a class of semiparametric goodness-of-fit tests. We consider the context of these papers, their contribution and their impact. Bickel’s first work on density estimation was carried out when this area was still in its infancy and proved to be highly influential for the subsequent wide-spread development of density and curve estimation and goodness-of-fit testing.

Hans-Georg Müller

Chapter 5. Adaptive Estimation

I discuss four papers of Peter Bickel and coauthors: Bickel (1982), Bickel and Klaassen (1986), Bickel and Ritov (1987), and Ritov and Bickel (1990).

Jon A. Wellner

Chapter 6. Boostrap Resampling

In this short article we discuss four of Peter Bickel’s seminal papers on theory and methodology for the bootstrap. We address the context of the work as well as its contributions and influence. The work began at the dawn of research on Efron’s bootstrap. In fact, Bickel and his co-authors were often the first to lay down the directions that others would follow when attempting to discover the strengths, and occasional weaknesses, of bootstrap methods.

Peter Hall

Chapter 7. High-Dimensional Statistics

Peter J. Bickel has made far-reaching and wide-ranging contributions to many areas of statistics. This short article highlights his marvelous contributions to high-dimensional statistical inference and machine learning, which range from novel methodological developments, deep theoretical analysis, and their applications. The focus is on the review and comments of his six recent papers in four areas, but only three of them are reproduced here due to limit of the space.

Jianqing Fan

Chapter 8. Miscellaneous

We introduce here four paper coauthored by P. J. Bickel. These papers have very little in common. Two of them can be considered mainly as papers dealing with concepts, while the two others are mainly tedious hard technical work that aims in developing complicated probabilistic results, which can be applied to the asymptotic theory of estimators.

Ya’acov Ritov


Jianqing Fan, Ya’acov Ritov, C. F. Jeff Wu
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