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Lectures on empirical processes. Theory and statistical applications. (English) Zbl 1132.62001

EMS Series of Lectures in Mathematics. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-027-2/pbk). ix, 254 p. (2007).
The theory of empirical processes constitutes the toolbox of mathematical techniques for people working in asymptotic statistics. The book consists of three lectures: Empirical and quantile processes in asymptotic theory of goodness-of-fit tests; Topics on empirical processes and Oracle inequalities and regularization. Techniques developed in the framework of probability in Banach spaces, Hungarian-type strong approximations, and tools from general stochastic process theory appear in connection with classical as well modern applications, such as goodness-of-fit tests, density estimation or general M-estimators. This book gives an excellent overview on the broad scope of the theory of empirical processes. It can be recommended for students and researchers interested in an advanced and well-documented approach to the selected topics.

MSC:

62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62G20 Asymptotic properties of nonparametric inference
62G30 Order statistics; empirical distribution functions
62-02 Research exposition (monographs, survey articles) pertaining to statistics
60F17 Functional limit theorems; invariance principles
62G10 Nonparametric hypothesis testing

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