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Lectures on Empirical Processes
EMS Series of Lectures in Mathematics

Eustasio del Barrio (Universidad de Valladolid, Spain)
Paul Deheuvels (Université de Paris VI, France)
Sara van de Geer (ETH Zürich, Switzerland)

Lectures on Empirical Processes

Theory and Statistical Applications

ISBN print 978-3-03719-027-2, ISBN online 978-3-03719-527-7
DOI 10.4171/027
January 2007, 263 pages, softcover, 17.0 x 24.0 cm.
39.50 Euro

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.

Further Information

Color pictures pp. 193–198

Review in Zentralblatt MATH 1132.62001

Review in MR 2284824

EMS Review