Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model \(AX=B\)
type: Item
instance of: scholarly article
title: Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model \(AX=B\)
zbMATH Open document ID: 1062.62100
published in: Metrika
publication date: 2004-09-22T00:00:00Z
review text: For a multivariate measurement error model, the authors consider the elementwise weighted total least squares (TLS) estimator. This problem covers the whole class of problems in which the errors in each element are proportional to its size and is therefore an important extension of the class of TLS problems studied so far. Some results proved by \textit{P. P. Gallo} [Commun. Stat. Theory Methods 11, 973--983 (1982; Zbl 0515.62064)] and \textit{L. J. Gleser} [Ann. Stat. 9, 24--44 (1981; Zbl 0496.62049)] are extended to the multivariate model. The approach is different. The errors are allowed to be unequally sized, consequently, it is impossible to derive an explicit formula for the estimator. It is shown that the estimator is the solution of an optimization problem. By analyzing the corresponding objective function, mild conditions for weak and strong consistency of the estimator are given. An iteratively reweighted numerical procedure is proposed.
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 65C60
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 2101693
zbMATH Keywords: linear errors-in-variables model
zbMATH Keywords: weighted total least squares estimator
zbMATH Keywords: multivariate model
zbMATH Keywords: consistency
zbMATH Keywords: numerical procedure
author: A. Kukush
author: Sabine Van Huffel
reviewed by: Liu Xinguo
MaRDI profile type: Publication
Recommended article: Q3104159
Recommended article: Consistency of the structured total least squares estimator in a multivariate errors-in-variables model
Recommended article: Asymptotic normality of element-wise weighted total least squares estimator in a multivariate errors-in-variables model
Recommended article: Q4940288
Recommended article: Q4530429
Recommended article: Consistency of the total least squares estimator in the linear errors-in-variables regression
Recommended article: Conditions for the consistency of the total least squares estimator in an errors-in-variables linear regression model
Recommended article: Consistent estimator in multivariate errors-in-variables model in the case of unknown error covariance structure
Recommended article: Consistent estimation for an errors-in-variables model based on constrained total least squares problems
Recommended article: Consistent estimation in the bilinear multivariate errors-in-variables model
description: scientific article; zbMATH DE number 2101693