## The Annals of Probability

### Weak convergence for weighted empirical processes of dependent sequences

#### Abstract

In this paper we establish weak convergence theorems for weighted empirical processes of strong mixing, $\rho$-mixing and associated sequences. We apply these results to obtain weak convergence of integral functionals of empirical processes and of mean residual life processes in reliability theory. To carry out the proofs, we develop two Rosenthal-type inequalities for strong mixing and associated sequences.

#### Article information

Source
Ann. Probab. Volume 24, Number 4 (1996), 2098-2127.

Dates
First available in Project Euclid: 6 January 2003

Permanent link to this document
http://projecteuclid.org/euclid.aop/1041903220

Digital Object Identifier
doi:10.1214/aop/1041903220

Mathematical Reviews number (MathSciNet)
MR1415243

Zentralblatt MATH identifier
0874.60006

#### Citation

Shao, Qi-Man; Yu, Hao. Weak convergence for weighted empirical processes of dependent sequences. Ann. Probab. 24 (1996), no. 4, 2098--2127. doi:10.1214/aop/1041903220. http://projecteuclid.org/euclid.aop/1041903220.

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