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October 1996 Weak convergence for weighted empirical processes of dependent sequences
Qi-Man Shao, Hao Yu
Ann. Probab. 24(4): 2098-2127 (October 1996). DOI: 10.1214/aop/1041903220

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.

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Qi-Man Shao. Hao Yu. "Weak convergence for weighted empirical processes of dependent sequences." Ann. Probab. 24 (4) 2098 - 2127, October 1996. https://doi.org/10.1214/aop/1041903220

Information

Published: October 1996
First available in Project Euclid: 6 January 2003

zbMATH: 0874.60006
MathSciNet: MR1415243
Digital Object Identifier: 10.1214/aop/1041903220

Subjects:
Primary: 60B10 , 60E15 , 60F15 , 60F17

Keywords: associated sequences , Integral functionals , mean residual life processes , mixing sequences , Rosenthal-type inequalities , weak convergence , weighted empirical processes

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 4 • October 1996
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