# Lectures on Empirical Processes: Theory and Statistical Applications

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*Eustasio del Barrio; Paul Deheuvels; Sara van de Geer*

A publication of the European Mathematical Society

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.