Weak convergence for weighted empirical processes of dependent sequences (Q674522)

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.