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

Abstract

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)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1971
Accession Number
AD0730462

Entities

People

  • J. S. Rao
  • Jayaram Sethuraman

Organizations

  • Florida State University

Tags

DTIC Thesaurus Topics

  • Convergence
  • Cooperation
  • Distribution Functions
  • Efficiency
  • Materials
  • Mathematics
  • Perturbations
  • Random Variables
  • Weak Convergence

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.

Technology Areas

  • Space