Empirical Processes: A Survey of Results for Independent and Identically Distributed Random Variables

Abstract

We consider a sequence $\xi_1, \xi_2, \cdots$ of independent and identically distributed random observations. Let $\mu_n$ denote the empirical distribution for the sample $\{\xi_1, \cdots, \xi_n\}$. It is the aim of the present article to give a survey of various results in the theory of empirical distributions and empirical processes. Special emphasis is given to the developments of the last ten years.