## The Annals of Probability

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

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

Peter Gaenssler and Winfried Stute

#### 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