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Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)



CONSISTENCY OF ORTHOGONAL REGRESSION ESTIMATOR IN IMPLICIT LINEAR ERRORS-IN-VARIABLES MODEL

O. O. Dashkov, A. G. Kukush

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Abstract: An implicit linear errors-in-variables model is considered, where the true points belong to a hyperplane in a Euclidean space and the total error variance-covariance matrix is proportional to the identity matrix. The orthogonal regression estimator of the hyperplane is studied. Sufficient conditions for the consistency and strong consistency of the estimator are presented. The results are applied to an explicit multiple errors-in-variables model with intercept.

Keywords: Consistent estimator, errors-in-variables model, implicit linear regression, multiple linear regression, orthogonal regression, total least squares

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