Asymptotic Independence of the Local Empirical Process Indexed by Functions

Abstract

We obtain independent joint strong approximations for multiple local empirical processes, which are independent of the approximation to the full empirical process. Applications include strong limit laws for iterated empirical processes.KeywordsRandom VectorEmpirical ProcessIterate LogarithmQuantile FunctionStrong ApproximationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.