This article is cited in 9 papers

Asymptotically optimal estimation in the linear regression problem in the case of violation of some classical assumptions

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 St. University, Khanty-Mansiisk

Abstract: We consider the problem of estimating the unknown parameters of linear regression in the case when the variances of observations depend on the unknown parameters of the model. A two-step method is suggested for constructing asymptotically linear estimators. Some general sufficient conditions for the asymptotic normality of the estimators are found, and an explicit form is established of the best asymptotically linear estimators. The behavior of the estimators is studied in detail in the case when the parameter of the regression model is one-dimensional.

Keywords: linear regression, two-step estimation, asymptotically normal estimator, best asymptotically linear estimator.

UDC: 519.237.5

Received: 02.11.2007

 English version: Siberian Mathematical Journal, 2009, 50:2, 302–315

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