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Lectures on empirical processes : Theory and statistical applications / Eustasio del Barrio, Paul Deheuvels, Sara van de Geer

Tác giả : Eustasio del Barrio, Paul Deheuvels, Sara van de Geer

Nhà xuất bản : European Mathematical Society

Năm xuất bản : 2007

Nơi xuất bản : Zurich, Switzerland

Mô tả vật lý : 254p. : ill. ; 24 cm.

ISBN : 9783037190272

Số phân loại : 516.3

Tùng thư : EMS series of lectures in mathematics

Chủ đề : 1. Thống kê toán -- Thuyết tiệm cận. 2. Mathematical statistics -- Asymptotic theory..

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Tóm tắt :

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.

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