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

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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.

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Authors and Affiliations

  1. Yugra State University, Khanty-Mansiĭsk, Russia

    A. I. Sakhanenko

  2. Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk, Russia

    Yu. Yu. Linke

Authors
  1. A. I. Sakhanenko
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  2. Yu. Yu. Linke
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Corresponding author

Correspondence to A. I. Sakhanenko.

Additional information

Original Russian Text Copyright © 2011 Sakhanenko A. I. and Linke Yu. Yu.

The authors were supported by the Russian Foundation for Basic Research (Grant 11-01-00285).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 4, pp. 894–912, July–August, 2011.

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Sakhanenko, A.I., Linke, Y.Y. Consistent estimation in a linear regression problem with random errors in coefficients. Sib Math J 52, 711–726 (2011). https://doi.org/10.1134/S0037446611040148

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  • DOI: https://doi.org/10.1134/S0037446611040148

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