On Berry-Esseen Rates for Statistical Functions, with Application to L-Estimates.

Abstract

A parameter expressed as a functional T(F) of a distribution function (d.f.) F may be estimated by the statistical function T(F sub n) based on the sample d.f. F sub n Typically, T(F sub n) is asymptotically normal. We investigate the rate of this convergence by utilizing the von Mises representation to express T(F sub n) - T (F) as an approximate U-statistic plus R sub n, and applying the Berry-Esseen rate 0(sq rt n) established for U-statistics by Callaert and Janssen. This essentially reduces the problem to a handling of R sub n. We carry out this method for linear functions of order statistics (L-estimates) and obtain results competitive with Bjerve and Helmers. Also, we briefly indicate the application of the method to M-estimates.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1979
Accession Number
ADA072131

Entities

People

  • Dennis D. Boos
  • Robert Serfling

Organizations

  • Florida State University

Tags

DTIC Thesaurus Topics

  • Computing-Related Activities
  • Convergence
  • Data Science
  • Distribution Functions
  • Functions (Mathematics)
  • Inequalities
  • Information Science
  • Military Research
  • Nonparametric Statistics
  • Normal Distribution
  • North Carolina
  • Order Statistics
  • Statistical Functions
  • Statistics
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Statistical inference.