Consistency of the total least squares estimator in the linear errors-in-variables regression
Volume 5, Issue 3 (2018), pp. 247–295
Pub. online: 30 May 2018
Type: Research Article
Open Access
Open Access
Received
31 October 2017
31 October 2017
Revised
7 May 2018
7 May 2018
Accepted
8 May 2018
8 May 2018
Published
30 May 2018
30 May 2018
Abstract
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.
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