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Title: Selected works of Peter J. Bickel Volume:
Author(s): Jianqing Fan; Ya'acov Ritov; Chien-Fu Wu
Series: Selected works in probability and statistics; Selected works in probability and statistics Periodical:
Publisher: Springer City: Princeton, New Jersey
Year: 2013 Edition:
Language: English Pages: 609
ISBN: 9781461455431, 146145543X, 9781461455448, 1461455448 ID: 925022
Time added: 2013-05-29 16:00:00 Time modified: 2013-10-24 01:16:58
Library: kolxoz Library issue: 63-64
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Foreword by Peter J. Bickel.- Preface.- Biography.- Publications.- Ph.D. Students.- Photos.- Rank-Based Nonparametrics.- Robust Statistics.- Asymptotic Theory.- Functional Estimation.- Adaptive Estimation.- Bootstrap Resampling.- High-Dimensional Statistics.- Miscellaneous
Preface
Our civilization depends largely on our ability to record major historical events,
such as philosophical thoughts, scientific discoveries, and technological inventions.
We manage these records through the collection, organization, presentation, and
analysis of past events. This allows us to pass our knowledge down to future
generations, to let them learn how our ancestors dealt with similar situations that
led to the outcomes we see today. The history of statistics is no exception. Despite
its long history of applications that have improved social wellbeing, systematic
studies of statistics to understand random phenomena are no more than a century
old. Many of our professional giants have devoted their lives to expanding the
frontiersofstatistics. Itisofparamountimportanceforustorecordtheirdiscoveries,
to understand the environments under which these discoveries were made, and to
assess their impacts on shaping the course of development in the statistical world.
It is with this backgroundthat we enthusiastically edit this volume.
Since obtaining his Ph.D. degree at the age of 22, Peter Bickel’s 50years of
distinguished work spans the revolution of scientific computing and data collection,
fromvacuumtubes forprocessingandsmallexperimentaldatato today’ssupercom-
puting and automated massive data scanning. The evolution of scientific computing
and data collection has a profound impact on statistical thinking, methodological
developments, and theoretical studies, thus creating evolving frontiers of statistics.
Peter Bickel has been a leading figure at the forefront of statistical innovations.
His career encompasses the majority of statistical developments in the last half-
century, which is about half of the entire history of the systematic development of
statistics. We therefore select some of his major papers at the frontiers of statistics
and reprint them here along with comments on their novelty and importance at that
time andtheir impactson thesubsequentdevelopment.We hopethat this will enable
future generations of statisticians to gain some insights on these exciting statistical
developments, help them understand the environment under which this research
was conducted, and inspire them to conduct their own research to address future
problems.
Peter Bickel’s research began with his thesis work on multivariate analysis
under the supervision of Erich Lehmann, followed by his work on robust statistics,
vii
viii Preface
semiparametric and nonparametricstatistics, and present work on high-dimensional
statistics. His workdemonstratestheevolutionofstatistics overthelast half-century,
from classical finite dimensional data in the 1960s and 1970s, to moderate-
dimensional data in the 1980s and 1990s, and to high-dimensional data in the first
decade of this century. His work exemplifies the idea that statistics as a discipline
grows stronger when it confronts the important problems of great social impact
while providinga fundamentalunderstandingofthese problemsandtheirassociated
methods that push forward theory, methodology, computation, and applications.
Because of the varied nature of Bickel’s work, it is a challenge to select his papers
for this volume. To help readers understand his contributions from a historical
prospective, we have divided his work into the following eight areas: “Rank-based
nonparametricstatistics”, “Robust statistics”, “Asymptotictheory”,“Nonparametric
function estimation”, “Adaptive and efficient estimation”, “Bootstrap and resam-
pling methods”, “High-dimensional statistical learning”, and “Miscellaneous”. The
division is imperfect and somewhat artificial. The work of a single paper can impact
the development of multiple areas. We acknowledge that omissions and negligence
are inevitable, but we hope to give readers a broad view on Bickel’s contributions.
This volume includes new photos of Peter Bickel, his biography,publication list,
and a list of his students. We hope this will give the readers a more complete picture
of Peter Bickel, as a teacher, a friend, a colleague, and a family man. We include a
short foreword by Peter Bickel in this volume.
We are honoredto have the opportunityto edit this Selected Work ofPeter Bickel
and to present his work to the readers. We are grateful to Peter Bühlmann, Peter
Hall, Hans-Georg Müeller, Qiman Shao, Jon Wellner, and Willem van Zwet for
their dedicated contributions to this volume. Without their in-depth comments and
prospects, this volume would not have been possible. We are grateful to Nancy
Bickel for her encouragement and support of this project, including the supply of
a majority of photos in this book. We would also like to acknowledge Weijie Gu,
Nina Guo, Yijie Dylan Wang, Matthias Tan and Rui Tuo for their help in typing
some of the comments, collecting of Bickel’s bibliography and list of students,
and typesetting the whole book. We are indebted to them for their hard work
and dedication. We would also like to thank Marc Strauss, Senior Editor, Springer
Science and Business Media, for his patience and assistance.
Princeton, NJ, USA Jianqing Fan
Jerusalem, Israel Ya’acov Ritov
Atlanta, GA, USA C.F. Jeff Wu
1 Rank-Based Nonparametrics ............................................... 1
Willem R. van Zwet and W. Albers
1.1 Introduction to Two Papers on Higher Order Asymptotics ........... 1
1.1.1 Introduction ..................................................... 1
1.1.2 Asymptotic Expansions for the Power of Distribution
Free Tests in the One-Sample Problem ........................ 1
Reprinted with permission of the Institute
of Mathematical Statistics
1.1.3 Edgeworth Expansions in Nonparametric Statistics .......... 7
Reprinted with permission of the Institute
of Mathematical Statistics
References ..................................................................... 9
2 Robust Statistics.............................................................. 51
Peter Bühlmann
2.1 Introduction to Three Papers on Robustness........................... 51
2.1.1 General Introduction............................................ 51
2.1.2 One-Step Huber Estimates in the Linear Model............... 51
Reprinted with permission of the American
Statistical Association
2.1.3 Parametric Robustness: Small Biases Can Be Worthwhile ... 52
Reprinted with permission of the Institute
of Mathematical Statistics
2.1.4 Robust Regression Based on Infinitesimal
Neighbourhoods ................................................ 53
Reprinted with permission of the Institute
of Mathematical Statistics
References ..................................................................... 53
ix
x Contents
3 Asymptotic Theory........................................................... 99
Qi-Man Shao
3.1 Introduction to Four Papers on Asymptotic Theory ................... 99
3.1.1 General Introduction............................................ 99
3.1.2 Asymptotic Theory of Bayes Solutions........................ 99
Reprinted with permission of Springer
Science+Business Media
3.1.3 The Bartlett Correction ......................................... 100
3.1.4 Asymptotic Distribution of the Likelihood Ratio
Statistic in Mixture Model ..................................... 102
Reprinted with permission of Wiley Eastern Limited
3.1.5 Hidden Markov Models ........................................ 103
Reprinted with permission of the Institute
of Mathematical Statistics
References ..................................................................... 105
4 Function Estimation ......................................................... 187
Hans-Georg Müller
4.1 Introduction to Three Papers on Nonparametric Curve Estimation... 187
4.1.1 Introduction ..................................................... 187
4.1.2 Density Estimation and Goodness-of-Fit ...................... 188
Reprinted with permission of the Institute
of Mathematical Statistics
4.1.3 Estimating Functionals of a Density ........................... 190
Reprinted with permission of the IndianStatistical
Institute
4.1.4 Curse of Dimensionality for Nonparametric
Regression on Manifolds ....................................... 192
Reprinted with permission of the Institute
of Mathematical Statistics
References ..................................................................... 193
5 Adaptive Estimation ......................................................... 243
Jon A. Wellner
5.1 Introduction to Four Papers on Semiparametric
and Nonparametric Estimation ......................................... 243
5.1.1 Introduction: Setting the Stage ................................. 243
5.1.2 Paper 1 .......................................................... 245
5.1.3 Paper 2 .......................................................... 246
5.1.4 Paper 3 .......................................................... 246
5.1.5 Paper 4 .......................................................... 247
5.1.6 Summary and Further Problems ............................... 248
References ..................................................................... 249
Contents xi
6 Boostrap Resampling........................................................ 333
Peter Hall
6.1 Introduction to Four Bootstrap Papers ................................. 333
6.1.1 Introduction and Summary ..................................... 333
6.1.2 Laying Foundations for the Bootstrap ......................... 334
6.1.3 The Bootstrap in Stratified Sampling .......................... 337
Reprinted with permission of the Institute
of Mathematical Statistics
6.1.4 Efficient Bootstrap Simulation ................................. 339
6.1.5 The m-Out-of-n Bootstrap...................................... 341
References ..................................................................... 343
7 High-Dimensional Statistics ................................................ 419
Jianqing Fan
7.1 Contributions of Peter Bickel to Statistical Learning.................. 419
7.1.1 Introduction ..................................................... 419
7.1.2 Intrinsic Dimensionality........................................ 420
7.1.3 Generalized Boosting........................................... 423
Reprinted with permission of the Journal
of Machine Learning Research
7.1.4 Variable Selections.............................................. 427
References ..................................................................... 428
8 Miscellaneous................................................................. 507
Ya’acov Ritov
8.1 Introduction to Four Papers by Peter Bickel ........................... 507
8.1.1 General Introduction............................................ 507
8.1.2 Minimax Estimation of the Mean of a Normal
Distribution When the Parameter Space Is Restricted ........ 507
Reprinted with permission of the Institute
of Mathematical Statistics
8.1.3 What Is a Linear Process? ...................................... 508
8.1.4 Sums of Functions of Nearest Neighbor Distances,
Moment Bounds, Limit Theorems and a Goodness
of Fit Test ....................................................... 509
Reprinted with permission of the Institute
of Mathematical Statistics
8.1.5 Convergence Criteria for Multiparameter
Stochastic Processes and Some Applications ................. 509
References ..................................................................... 510
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