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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 1, Pages 128–145
(Mi smj2072)
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This article is cited in 6 scientific papers (total in 6 papers)
Asymptotically optimal estimation in a linear regression problem with random errors in coefficients
Yu. Yu. Linkea, A. I. Sakhanenkob a 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.
Received: 28.10.2008
Citation:
Yu. Yu. Linke, A. I. Sakhanenko, “Asymptotically optimal estimation in a linear regression problem with random errors in coefficients”, Sibirsk. Mat. Zh., 51:1 (2010), 128–145; Siberian Math. J., 51:1 (2010), 104–118
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https://www.mathnet.ru/eng/smj2072 https://www.mathnet.ru/eng/smj/v51/i1/p128
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Abstract page: | 294 | Full-text PDF : | 69 | References: | 45 | First page: | 1 |
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