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Lectures on Empirical Processes: Theory and Statistical Applications
Eustasio del Barrio, Universidad de Valladolid, Spain, Paul Deheuvels, Université de Paris VI, Bourg-la-Reine, France, and Sara van de Geer, ETH Zentrum, Zurich, Switzerland
A publication of the European Mathematical Society.
cover
EMS Series of Lectures in Mathematics
2007; 264 pp; softcover
Volume: 6
ISBN-10: 3-03719-027-2
ISBN-13: 978-3-03719-027-2
List Price: US$48
Member Price: US$38.40
Order Code: EMSSERLEC/6
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The theory of empirical processes constitutes the mathematical toolbox of asymptotic statistics. Its growth was accelerated by the 1950s work on the Functional Central Limit Theorem and the Invariance Principle. The theory has developed in parallel with statistical methodologies, and has been successfully applied to a large diversity of problems related to the asymptotic behaviour of statistical procedures.

The three sets of lecture notes in the book offer a wide panorama of contemporary empirical processes theory. Techniques are developed in the framework of probability in Banach spaces, Hungarian-style strong approximations, using tools from general stochastic process theory. Other tools appear in this text in connection with historical as well as modern applications, such as goodness-of-fit tests, density estimation or general M-estimators.

This book gives an excellent overview of the broad scope of the theory of empirical processes. It will be an invaluable aid for students and researchers interested in an advanced and well-documented approach to the selected topics.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in probability.

Table of Contents

  • E. del Barrio -- Empirical and quantile processes in the asymptotic theory of goodness-of-fit tests
  • P. Deheuvels -- Topics on empirical process
  • S. van de Geer -- Oracle inequalities and regularization
  • Index
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