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A central limit theorem for empirical processes

Part of: Limit theorems

Published online by Cambridge University Press:  09 April 2009

David Pollard
David Pollard
Affiliation:
Department of Statistics Yale UniversityNew Haven, Connecticut 06520, U.S.A.
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Abstract

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The empirical measure Pn for independent sampling on a distribution P is formed by placing mass n−1 at each of the first n sample points. In this paper, n½(Pn − P) is regarded as a stochastic process indexed by a family of square integrable functions. A functional central limit theorem is proved for this process. The statement of this theorem involves a new form of combinatorial entropy, definable for classes of square integrable functions.

Keywords

empirical measureDonsker class of functionscombinatorial entropyweak convergence of empirical processescentral limit theoremsymmetrizationseparable stochastic processes.

MSC classification

Secondary: 60F05: Central limit and other weak theorems 60F17: Functional limit theorems; invariance principles

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 2 , October 1982 , pp. 235 - 248
Copyright
Copyright © Australian Mathematical Society 1982

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