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Theory of estimation of parameters in a linear regression scheme

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Abstract

Fairly simple asymptotically optimal equivariant polynomial estimators of any degree k are constructed for the parameters of a standard linear regression scheme whose design matrix satisfies a certain additional condition. These estimators depend on the error distribution function only in terms of its first 2K moments. An explicit equation for an optimal equivariant quadratic estimator of parameters is also presented.

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Authors
  1. A. V. Kakosyan
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 53, pp. 118–129, 1975.

The author express his gratitude to A. M. Kagan for posing the problem and for his interest.

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Kakosyan, A.V. Theory of estimation of parameters in a linear regression scheme. J Math Sci 12, 227–237 (1979). https://doi.org/10.1007/BF01262721

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  • DOI: https://doi.org/10.1007/BF01262721

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