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 asymptotic efficiencies of tests based on spacings, need to study the weak convergence of empirical distribution functions of random variables subject to random perturbations and scale factors was found. This problem is studied in this paper.