The Annals of Probability

Weak convergence for weighted empirical processes of dependent sequences

Qi-Man Shao and Hao Yu

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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.

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

First available in Project Euclid: 6 January 2003

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Primary: 60B10: Convergence of probability measures 60F15: Strong theorems 60E15: Inequalities; stochastic orderings 60F17: Functional limit theorems; invariance principles

Weak convergence weighted empirical processes integral functionals mixing sequences associated sequences mean residual life processes Rosenthal-type inequalities


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.

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