## The Annals of Probability

### Properties of the Empirical Distribution Function for Independent Non- Identically Distributed Random Vectors

Martien C. A. van Zuijlen

#### Abstract

A generalization to the case of independent but not necessarily identically distributed two-dimensional underlying random vectors is obtained of results on univariate empirical df's of van Zuijlen (1976) (linear bounds), Ghosh (1972) and Ruymgaart and van Zuijlen (1978b). No conditions are imposed on the dependence structure of the underlying df's. In the process improvements of van Zuijlen's results concerning linear bounds in the univariate non-i.i.d. case are obtained, whereas also applications of the results on multivariate empirical df's are discussed. Extensions of the two-dimensional results to the $k$-dimensional case $(k > 2)$ are straightforward and therefore omitted.

#### Article information

Source
Ann. Probab., Volume 10, Number 1 (1982), 108-123.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176993916

Digital Object Identifier
doi:10.1214/aop/1176993916

Mathematical Reviews number (MathSciNet)
MR637379

Zentralblatt MATH identifier
0482.60038

JSTOR