Consistency of the total least squares estimator in the linear errors-in-variables regression

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.

Prediction in polynomial errors-in-variables models

“…The random vector e models the error in the regression equation, and ǫ models the measurement error in y; ǫ can be correlated with δ. Such models are studied, e.g., in [11,10,9] in relation to system identification problems and numerical linear algebra. We list the model assumptions.…”