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

Shklyar, Sergiy

doi:10.15559/18-vmsta104

Cited by 2 publications

(1 citation statement)

References 18 publications

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“…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.…”

Section: Model and Main Assumptionsmentioning

confidence: 99%

Prediction in polynomial errors-in-variables models

Kukush¹,

Sen’ko²

2020

Modern Stochastics: Theory and Applications

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A multivariate errors-in-variables (EIV) model with an intercept term, and a polynomial EIV model are considered. Focus is made on a structural homoskedastic case, where vectors of covariates are i.i.d. and measurement errors are i.i.d. as well. The covariates contaminated with errors are normally distributed and the corresponding classical errors are also assumed normal. In both models, it is shown that (inconsistent) ordinary least squares estimators of regression parameters yield an a.s. approximation to the best prediction of response given the values of observable covariates. Thus, not only in the linear EIV, but in the polynomial EIV models as well, consistent estimators of regression parameters are useless in the prediction problem, provided the size and covariance structure of observation errors for the predicted subject do not differ from those in the data used for the model fitting.

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Section: Model and Main Assumptionsmentioning

confidence: 99%