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February, 1982 Properties of the Empirical Distribution Function for Independent Non- Identically Distributed Random Vectors
Martien C. A. van Zuijlen
Ann. Probab. 10(1): 108-123 (February, 1982). DOI: 10.1214/aop/1176993916

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.

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Martien C. A. van Zuijlen. "Properties of the Empirical Distribution Function for Independent Non- Identically Distributed Random Vectors." Ann. Probab. 10 (1) 108 - 123, February, 1982. https://doi.org/10.1214/aop/1176993916

Information

Published: February, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0482.60038
MathSciNet: MR637379
Digital Object Identifier: 10.1214/aop/1176993916

Subjects:
Primary: 60G17
Secondary: 62G30

Keywords: Empirical distribution function , linear bounds , multivariate non-i.i.d. case

Rights: Copyright © 1982 Institute of Mathematical Statistics

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Vol.10 • No. 1 • February, 1982
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