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

Joel E Michalek

doi:10.1080/03610927608827347

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

Research output: Contribution to journal › Article › peer-review

Abstract

An empirical distribution function F_m, 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 F_m are established. The relative efficiency of F_m as compared to the classical empirical distribution function is calculated and tabled-for n = 10, 20, 50, 100, 200.

Original language	English (US)
Pages (from-to)	241-250
Number of pages	10
Journal	Communications in Statistics - Theory and Methods
Volume	5
Issue number	3
DOIs	https://doi.org/10.1080/03610927608827347
State	Published - Jan 1 1976
Externally published	Yes

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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10.1080/03610927608827347

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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.",

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AB - 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.

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KW - empirical distribution function

KW - one and two sided deviations

KW - relative efficiency

KW - selected order statistics

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

Abstract

Keywords

ASJC Scopus subject areas

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