Weak Convergence of Empirical Distribution Functions of Random Variables Subject to Perturbations and Scale Factors.

摘要

The weak convergence of empirical distribution functions of independent identically distributed random variables is well-known and has been studied by several authors notably Doob (1949) and Donsker (1951. In an earlier paper, Sethuraman and Rao (1970),while studying the asympototic efficiencies of tests based on spacings the authors found a need to study the weak convergence of empirical distribution functions of random variables subject to random perturbations and scale factors. The authors study this problem in this paper. The material of this paper is divided into two sections. Section 2treats the aforementioned problem and is independent of Sethuraman and Rao (1970). Section 3shows how one can use the weak convergence results of Section 1in problems connected with spacings thus relating the present work to Sethuraman and Rao (1970). (Author)