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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 4, Pages 894–912 (Mi smj2246)  
This article is cited in 3 scientific papers (total in 3 papers)

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

A. I. Sakhanenkoa, Yu. Yu. Linkebc

a Yugra State University, Khanty-Mansiĭsk, Russia
b Sobolev Institute of Mathematics, Novosibirsk, Russia
c Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (345 kB) Citations (3)
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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.
Keywords: linear regression, errors in independent variables, replicated regressors, dependence of variances on a parameter, two-step estimates, consistent estimate, asymptotically normal estimate.
Received: 13.01.2011
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 4, Pages 711–726
DOI: https://doi.org/10.1134/S0037446611040148
Bibliographic databases:
Document Type: Article
UDC: 519.233.5
Language: Russian
Citation: A. I. Sakhanenko, Yu. Yu. Linke, “Consistent estimation in a linear regression problem with random errors in coefficients”, Sibirsk. Mat. Zh., 52:4 (2011), 894–912; Siberian Math. J., 52:4 (2011), 711–726
Citation in format AMSBIB
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\by A.~I.~Sakhanenko, Yu.~Yu.~Linke
\paper Consistent estimation in a~linear regression problem with random errors in coefficients
\jour Sibirsk. Mat. Zh.
\yr 2011
\vol 52
\issue 4
\pages 894--912
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\transl
\jour Siberian Math. J.
\yr 2011
\vol 52
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\pages 711--726
\crossref{https://doi.org/10.1134/S0037446611040148}
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Linking options:
  • https://www.mathnet.ru/eng/smj2246
  • https://www.mathnet.ru/eng/smj/v52/i4/p894
    • This publication is cited in the following 3 articles:
    1. Yu. Yu. Linke, A. I. Sakhanenko, “On asymptotics of the distributions of some two-step statistical estimators of a mutlidimensional parameter”, Siberian Adv. Math., 24:2 (2014), 119–139  mathnet  crossref  mathscinet  elib
    2. Yu. Yu. Linke, A. I. Sakhanenko, “Ob asimptotike raspredeleniya dvukhshagovykh statisticheskikh otsenok odnomernogo parametra”, Sib. elektron. matem. izv., 10 (2013), 627–640  mathnet
    3. Yu. Yu. Linke, “On the asymptotics of distributions of two-step statistical estimates”, Siberian Math. J., 52:4 (2011), 665–681  mathnet  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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