Consistency of the total least squares estimator in the linear errors-in-variables regression
Open Access
- 30 May 2018
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 5 (3), 247-295
- https://doi.org/10.15559/18-vmsta104
Abstract
Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: Consistency of the total least squares estimator in the linear errors-in-variables regression, Authors: Sergiy Shklyar , This paper deals with a homoskedastic errors-in-variables linear regression model and properties of the total least squares (TLS) estimator. We partly revise the consistency results for the TLS estimator previously obtained by the author [18]. We present complete and comprehensive proofs of consistency theorems. A theoretical foundation for construction of the TLS estimator and its relation to the generalized eigenvalue problem is explained. Particularly, the uniqueness of the estimate is proved. The Frobenius norm in the definition of the estimator can be substituted by the spectral norm, or by any other unitarily invariant norm; then the consistency results are still valid.Keywords
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