The Annals of Probability

Empirical Processes: A Survey of Results for Independent and Identically Distributed Random Variables

Peter Gaenssler and Winfried Stute

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Abstract

We consider a sequence $\xi_1, \xi_2, \cdots$ of independent and identically distributed random observations. Let $\mu_n$ denote the empirical distribution for the sample $\{\xi_1, \cdots, \xi_n\}$. It is the aim of the present article to give a survey of various results in the theory of empirical distributions and empirical processes. Special emphasis is given to the developments of the last ten years.

Article information

Source
Ann. Probab. Volume 7, Number 2 (1979), 193-243.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995085

Digital Object Identifier
doi:10.1214/aop/1176995085

Mathematical Reviews number (MathSciNet)
MR525051

Zentralblatt MATH identifier
0402.60031

JSTOR
links.jstor.org

Subjects
Primary: 62D05: Sampling theory, sample surveys
Secondary: 60B10: Convergence of probability measures 60F05: Central limit and other weak theorems 60F10: Large deviations 60F15: Strong theorems 60K99: None of the above, but in this section 62E15: Exact distribution theory 60E20

Keywords
60-02 Empirical distribution empirical process Glivenko-Cantelli convergence LIL's for empirical processes weighted empirical process invariance principle rates of convergence random sample size strong approximation

Citation

Gaenssler, Peter; Stute, Winfried. Empirical Processes: A Survey of Results for Independent and Identically Distributed Random Variables. Ann. Probab. 7 (1979), no. 2, 193--243. doi:10.1214/aop/1176995085. https://projecteuclid.org/euclid.aop/1176995085


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