Weak Convergence of Empirical Distribution Functions of Random Variables Subject to Perturbations and Scale Factors.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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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 2 treats the aforementioned problem and is independent of Sethuraman and Rao 1970. Section 3 shows how one can use the weak convergence results of Section 1 in problems connected with spacings thus relating the present work to Sethuraman and Rao 1970. Author
- Statistics and Probability