This article is cited in 5 papers

Improvement of estimators in a linear regression problem with random errors in coefficients

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

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

Abstract: Under consideration is the problem of estimating the linear regression parameter in the case when the variances of observations depend on the unknown parameter of the model, while the coefficients (independent variables) are measured with random errors. We propose a new two-step procedure for constructing estimators which guarantees their consistency, find general necessary and sufficient conditions for the asymptotic normality of these estimators, and discuss the case in which these estimators have the minimal asymptotic variance.

Keywords: linear regression, errors in the independent variables, dependence of variance on a parameter, two-step estimation, asymptotically normal estimator.

UDC: 519.237.5

Received: 20.11.2009
Revised: 26.10.2010

 English version: Siberian Mathematical Journal, 2011, 52:1, 113–126

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