Asymptotically optimal estimation in a linear regression problem with random errors in coefficients |
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Authors: | Yu Yu Linke A I Sakhanenko |
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Institution: | (3) GVCS, BASF Aktiengesellschaft, Ludwigshafen, Germany; |
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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. |
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Keywords: | |
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