Bootstraps of sums of independent but not identically distributed stochastic processes
A central limit theorem for sums of independent, but not identically distributed stochastic processes multiplied by independent real random variables with mean zero is developed. Weak convergence of the Hoffmann-Jorgensen-Dudley type, as described by \textit{A. van der Vaart} and \textit{J. A. Wellner} [Weak convergence and empirical processes. With applications to statistics. (1996; Zbl 0862.60002)], is utilized. These results allow Monte Carlo estimation of limiting probability measures obtained from application of \textit{D. Pollard} 's [Empirical processes: theory and applications. (1990; Zbl 0741.60001)] functional central limit theorem for empirical processes. An application of this theory to the two-parameter Cox score process with staggered entry data is given for illustration. For this process, the proposed multiplier bootstrap appears to be the first successful method for estimating the associated limiting distribution. The results of this paper complement previous bootstrap and multiplier central limit theorems for i.i.d. empirical processes. The references contain 17 bibliographical hints.
Hoffmann-Jorgensen-Dudley weak convergence
scientific article; zbMATH DE number 1912390