The influence function in the errors in variables problem
type: Item
instance of: scholarly article
title: The influence function in the errors in variables problem
zbMATH Open document ID: 0558.62065
author: Gabrielle Kelly
published in: The Annals of Statistics
publication date: 1984-01-01T00:00:00Z
review text: The paper deals with the problem of variance estimation of some parameter vector estimators in the model \(z_ i=u_ i+e_ i\), \(i=1,...,n\), where the components of \(u_ i\) are linearly related: \(u_{2i}=\alpha +\beta u_{1i}\); \(u_ i\), \(e_ i\) are i.i.d. variables and are independent; the ratio of error variances is known; the common distribution of \(z_ i\) admits fourth order moments. The influence function of an estimator is calculated and used to calculate its asymptotic covariance matrix. The connection with estimation in the linear regression model is considered. The behaviour of some classical estimators is investigated by Monte Carlo methods. A numerical example taken from the literature is used to illustrate the rôle of the influence function in detection of influential observations.
Mathematics Subject Classification ID: 62J99
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 3890557
zbMATH Keywords: errors in variables problem
zbMATH Keywords: jackknife
zbMATH Keywords: boot-strap
zbMATH Keywords: normal theory
zbMATH Keywords: influence function
zbMATH Keywords: asymptotic covariance matrix
zbMATH Keywords: detection of influential observations
reviewed by: Emiliana Ursianu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346394
OpenAlex ID: W2016412712
DOI: 10.1214/AOS/1176346394
description: scientific article; zbMATH DE number 3890557