On \(L_ p\)-convergence rates for statistical functions with application to L-estimates
type: Item
instance of: scholarly article
title: On \(L_ p\)-convergence rates for statistical functions with application to L-estimates
zbMATH Open document ID: 0563.62013
DOI: 10.1007/BF02480996
author: I. A. Ahmad
published in: Annals of the Institute of Statistical Mathematics
publication date: 1983-01-01T00:00:00Z
review text: A parameter which may be represented as a functional T(F) of a distribution function F may be estimated by the ''statistical function'' \(T(F_ n)\), where \(F_ n\) is the empirical distribution function. Recently, \textit{D. D. Boos} and \textit{R. J. Serfling} [On Berry-Esseen rates for statistical functions with application to L-estimates. Florida State Univ. Stat. Rep. No.M 499 (1979)] obtained sufficient conditions for the Berry-Esseen theorem to hold for \(T(F_ n)-T(F)\) and applied the results to derive rates of convergence in \(L_{\infty}\) for L-estimates. The present note complements their work by obtaining the \(L_ p\)-rates of convergence, \(1\leq p<\infty\) for \(T(F_ n)-T(F)\) and its application to L-estimates.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62F05
zbMATH DE Number: 3898009
zbMATH Keywords: U statistics
zbMATH Keywords: L sub(p) convergence rates
zbMATH Keywords: statistical function
zbMATH Keywords: empirical distribution
zbMATH Keywords: Berry-Esseen theorem
zbMATH Keywords: L-estimates
MaRDI profile type: Publication
cites work: Q3921974
cites work: The Berry-Esseen theorem for U-statistics
cites work: A nonuniform bound on convergence to normality
cites work: On the Accuracy of Gaussian Approximation to the Distribution Functions of Sums of Independent Variables
cites work: On the Asymptotic Distribution of Differentiable Statistical Functions
full work available at URL: https://doi.org/10.1007/bf02480996
OpenAlex ID: W2065788186
description: scientific article; zbMATH DE number 3898009