The element-wise weighted total least-squares problem

DOI10.1016/j.csda.2004.07.014zbMath1429.62298OpenAlexW2097583558MaRDI QIDQ959147

Amedeo Premoli, Ivan Markovsky, Maria Luisa Rastello, Alexander G. Kukush, Sabine Van Huffel

Publication date: 11 December 2008

Published in: Computational Statistics and Data Analysis (Search for Journal in Brave)

Full work available at URL: https://eprints.soton.ac.uk/263293/1/ewtls_published.pdf

zbMATH Keywords

non-convex optimizationtotal least squaresmultivariate errors-in-variables modelre-weighted least-squaresunequally sized errors

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Linear regression; mixed models (62J05) Numerical solutions to overdetermined systems, pseudoinverses (65F20)

Related Items (13)

Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model \(AX = B\) ⋮ EIV-based interference alignment scheme with CSI uncertainties ⋮ Left vs, right representations for solving weighted low-rank approximation problems ⋮ EIV regression with bounded errors in data: total `least squares' with Chebyshev norm ⋮ TLS-EM algorithm of mixture density models for exponential families ⋮ Approximate low-rank factorization with structured factors ⋮ 2nd special issue on matrix computations and statistics ⋮ Incremental method for multiple line detection problem -- iterative reweighted approach ⋮ Consistency of the structured total least squares estimator in a multivariate errors-in-variables model ⋮ Editorial: Total least squares and errors-in-variables modeling ⋮ Local influence assessment in heteroscedastic measurement error models ⋮ Perturbation analysis and condition numbers of scaled total least squares problems ⋮ Detecting and isolating abrupt changes in linear switching systems

Cites Work

• An Analysis of the Total Least Squares Problem
• Structured total least squares and \(L_ 2\) approximation problems
• Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model \(AX=B\)
• Consistency of regression estimates when some variables are subject to error
• Analysis and Properties of the Generalized Total Least Squares Problem $AX \approx B$ When Some or All Columns in A are Subject to Error
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