Weak convergence for weighted empirical processes of dependent sequences. (English) Zbl 0874.60006
Weak convergence theorems for weighted empirical processes based on strictly stationary observations under strong mixing, \(\rho\)-mixing and associated dependence assumptions are established. Weak convergence of integral type functionals of empirical processes and of mean residual life processes in reliability theory are obtained. Two Rosenthal-type inequalities for \(\alpha\)-mixing and associated sequences are proved. These inequalities are also of independent interest.
Reviewer: A.J.Rachkauskas (Vilnius)
MSC:
| 60B10 | Convergence of probability measures |
| 60F17 | Functional limit theorems; invariance principles |
| 60F15 | Strong limit theorems |
| 60E15 | Inequalities; stochastic orderings |
Keywords:
Weak convergence; weighted empirical processes; integral functionals; mixing sequences; associated sequences; mean residual life processes; Rosenthal-type inequalities; reliability theoryReferences:
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