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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.

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