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Consistency of the total least squares estimator in the linear errors-in-variables regression. (English) Zbl 1417.62196
Summary: 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 [Theory Probab. Math. Stat. 83, 175–190 (2011; Zbl 1328.62345); translation from Teor. Jmovirn. Mat. Stat. 83, 148–162 (2010)]. 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.

MSC:
62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
62F12 Asymptotic properties of parametric estimators
Software:
VanHuffel
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References:
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