Uniform Convergence Of An Empirical Cdf Based On A Relatively Small Number Of Order Statistics

Joel E Michalek

Research output: Contribution to journalArticlepeer-review

Abstract

An empirical distribution function Fm, defined on a subset of order statistics of a random sample of size n taken from the distribution of a random variable with continuous distribution function F, is shown to converge uniformly with probability one to F. Small sample distributions of the one and two sided deviations and the asymptotic normality of the standardized Fm are established. The relative efficiency of Fm as compared to the classical empirical distribution function is calculated and tabled-for n = 10, 20, 50, 100, 200.

Original languageEnglish (US)
Pages (from-to)241-250
Number of pages10
JournalCommunications in Statistics - Theory and Methods
Volume5
Issue number3
DOIs
StatePublished - Jan 1 1976
Externally publishedYes

Keywords

  • asymptotic normality
  • empirical distribution function
  • one and two sided deviations
  • relative efficiency
  • selected order statistics

ASJC Scopus subject areas

  • Statistics and Probability

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