The Annals of Probability
- Ann. Probab.
- Volume 10, Number 1 (1982), 108-123.
Properties of the Empirical Distribution Function for Independent Non- Identically Distributed Random Vectors
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.
Ann. Probab., Volume 10, Number 1 (1982), 108-123.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G17: Sample path properties
Secondary: 62G30: Order statistics; empirical distribution functions
van Zuijlen, Martien C. A. Properties of the Empirical Distribution Function for Independent Non- Identically Distributed Random Vectors. Ann. Probab. 10 (1982), no. 1, 108--123. doi:10.1214/aop/1176993916. https://projecteuclid.org/euclid.aop/1176993916