Selected Works in Probability and Statistics

Selected Works of R.M. Dudley

Editors: Giné, Evarist, Koltchinskii, Vladimir, Norvaiša, R. (Eds.)

  • Includes his major journal publications plus commentaries in the papers by the editors
  • Includes a complete bibliography
  • Electronic version is freely available on SpringerLink
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About this book

For almost fifty years, Richard M. Dudley has been extremely influential in the development of several areas of Probability. His work on Gaussian processes led to the understanding of the basic fact that their sample boundedness and continuity should be characterized in terms of proper measures of complexity of their parameter spaces equipped with the intrinsic covariance metric. His sufficient condition for sample continuity in terms of metric entropy is widely used and was proved by X. Fernique to be necessary for stationary Gaussian processes, whereas its more subtle versions (majorizing measures) were proved by M. Talagrand to be necessary in general.

Together with V. N. Vapnik and A. Y. Cervonenkis, R. M. Dudley is a founder of the modern theory of empirical processes in general spaces. His work on uniform central limit theorems (under bracketing entropy conditions and for Vapnik-Cervonenkis classes), greatly extends classical results that go back to A. N. Kolmogorov and M. D. Donsker, and became the starting point of a new line of research, continued in the work of Dudley and others, that developed empirical processes into one of the major tools in mathematical statistics and statistical learning theory.

As a consequence of Dudley's early work on weak convergence of probability measures on non-separable metric spaces, the Skorohod topology on the space of regulated right-continuous functions can be replaced, in the study of weak convergence of the empirical distribution function, by the supremum norm. In a further recent step Dudley replaces this norm by the stronger p-variation norms, which then allows replacing compact differentiability of many statistical functionals by Fréchet differentiability in the delta method.

Richard M. Dudley has also made important contributions to mathematical statistics, the theory of weak convergence, relativistic Markov processes, differentiability of nonlinear operators and several other areas of mathematics.

Professor Dudley has been the adviser to thirty PhD's and is a Professor of Mathematics at the Massachusetts Institute of Technology.

Reviews

From the reviews:

“This book is comprised of a number of Professor R. M. Dudley’s best works … . Each part begins with an introduction followed by a number of papers written by Dudley and his co-researchers. … The book also presents a biographical sketch of Dudley and provides his bibliography (1961–2009). … This is a comprehensive collection of work within mathematical statistics and probability theory and will be of special interest to graduate students and researchers in probability, statistics and related fields.” (Technometrics, Vol. 53 (2), May, 2011)


Table of contents (29 chapters)

  • Introduction

    Giné, Evarist (et al.)

    Pages 3-4

  • Weak Convergence of Probabilities on Nonseparable Metric Spaces and Empirical Measures on Euclidean Spaces

    Dudley, R. M.

    Pages 5-22

  • Measures on Non-Separable Metric Spaces

    Dudley, R. M.

    Pages 23-27

  • Distances of Probability Measures and Random Variables

    Dudley, R. M.

    Pages 28-37

  • An Extended Wichura Theorem, Definitions of Donsker Class, and Weighted Empirical Distributions

    Dudley, R. M.

    Pages 38-75

Buy this book

eBook $199.00
price for USA (gross)
  • ISBN 978-1-4419-5821-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $259.00
price for USA
  • ISBN 978-1-4419-5820-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Selected Works of R.M. Dudley
Editors
  • Evarist Giné
  • Vladimir Koltchinskii
  • R. Norvaiša
Series Title
Selected Works in Probability and Statistics
Copyright
2010
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4419-5821-1
DOI
10.1007/978-1-4419-5821-1
Hardcover ISBN
978-1-4419-5820-4
Series ISSN
2197-5825
Edition Number
1
Number of Pages
XXIV, 481
Topics