Approximations for hybrids of empirical and partial sums processes (Q1578213)

The author derives probability inequalities and almost sure rates for approximations of hybrids of empirical and partial sums processes. Actually, he shows that replacing the random time change in results proved by \textit{J. Diebolt} [J. Stat. Plann. Inference 44, No.~1, 1--17 (1995; Zbl 0812.62051)] by a non-random time change does not alter the rates of the approximations. Further, the proofs are based on Poisson approximations for empirical processes and Gaussian approximations for randomly stopped partial sums.