Estimation of influence functions
type: Item
instance of: scholarly article
title: Estimation of influence functions
zbMATH Open document ID: 0612.62045
DOI: 10.1016/0167-7152(86)90022-2
author: Murray D. Burke
author: Lajos Horváth
published in: Statistics \& Probability Letters
publication date: 1986-01-01T00:00:00Z
review text: The influence function of an estimator is used for mainly two purposes: to indicate the sensitivity of the estimator to particular values and for computing the asymptotic variance of the estimator. Empirical versions of the influence function have been used to indicate influential data points in a particular sample and for constructing variance estimators. In this article influence functions for L-estimators (i.e. linear combinations of order statistics) are considered. In particular, weak approximation theorems for an empirical influence function and for its bootstrapped version are proved. Further, it is indicated how the latter can be used to derive asymptotic confidence bounds for the unknown influence function. Finally, the authors point out that the presented method for treating influence function estimates of L-estimators also works for other estimators such as M- and R-estimators and for U-statistics.
reviewed by: Hans Nyquist
Mathematics Subject Classification ID: 62F35
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 3990622
zbMATH Keywords: goodness-of-fit
zbMATH Keywords: empirical distribution function
zbMATH Keywords: weak convergence
zbMATH Keywords: bootstrapped influence functions
zbMATH Keywords: L-estimators
zbMATH Keywords: weak approximation theorems
zbMATH Keywords: empirical influence function
zbMATH Keywords: asymptotic confidence bounds
MaRDI profile type: Publication
full work available at URL: 0167-7152(86)90022-2
OpenAlex ID: W2060486836
cites work: Weighted empirical and quantile processes
cites work: Bootstrapping empirical functions
cites work: Q3857500
cites work: Robust Statistics
cites work: Limit theorems for the ratio of the empirical distribution function to the true distribution function
Recommended article: Estimators of Influence Function
Recommended article: Influence function and correspondence analysis
Recommended article: Robust inference by influence functions
Recommended article: The influence function of semiparametric estimators
Recommended article: On the estimation of the influence curve
Recommended article: Influence function analysis applied to partial least squares
Recommended article: Influence analysis for generalized estimating equations
Recommended article: Q4011496
description: scientific article; zbMATH DE number 3990622