This article is cited in 3 papers

Consistent estimation in a linear regression problem with random errors in coefficients

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

a</sup> Yugra State University, Khanty-Mansiĭsk, Russia
^b Sobolev Institute of Mathematics, Novosibirsk, Russia
^c Novosibirsk State University, Novosibirsk, Russia

Abstract: We consider the linear regression model in the case when the independent variables are measured with errors, while the variances of the main observations depend on an unknown parameter. In the case of normally distributed replicated regressors we propose and study new classes of two-step estimates for the main unknown parameter. We find consistency and asymptotic normality conditions for first-step estimates and an asymptotic normality condition for second-step estimates. We discuss conditions under which these estimates have the minimal asymptotic variance.

Keywords: linear regression, errors in independent variables, replicated regressors, dependence of variances on a parameter, two-step estimates, consistent estimate, asymptotically normal estimate.

UDC: 519.233.5

Received: 13.01.2011

 English version: Siberian Mathematical Journal, 2011, 52:4, 711–726

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