This article is cited in 6 papers

Asymptotically optimal estimation in a linear regression problem with random errors in coefficients

Yu. Yu. Linke^a, A. I. Sakhanenko<sup>b

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Ugra State University, Khanty-Mansiisk

Abstract: We consider the problem of estimating an unknown one-dimensional parameter in the linear regression problem in the case when the independent variables (called coefficients in the article) are measured with errors, and the variances of the principal observations can depend on the main parameter. We study the behavior of two-step estimators, previously introduced by the authors, which are asymptotically optimal in the case when the independent variables are measured without errors. Under sufficiently general assumptions we find necessary and sufficient conditions for the asymptotic normality and asymptotic optimality of these estimators in the new setup.

Keywords: linear regression, errors in the independent variables, two-step estimation, asymptotically normal estimator.

UDC: 519.233.5

Received: 28.10.2008

 English version: Siberian Mathematical Journal, 2010, 51:1, 104–118

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