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Condition for the constancy of regression of a polynomial statistic on a sample mean

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Abstract

Conditions are obtained, under which from the constancy of the regression of a polynomial statistic of independent random variables on a sample mean there follows that the characteristic functions of the considered random variables are entire and of finite order. There are given also conditions on a polynomial statistic that are sufficient for the characterization of a normal distribution by the property of the constancy of the regression of this statistic on a sample mean.

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Authors
  1. A. A. Zinger
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  2. L. B. Klebanov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 106–114, 1990.

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Zinger, A.A., Klebanov, L.B. Condition for the constancy of regression of a polynomial statistic on a sample mean. J Math Sci 68, 469–474 (1994). https://doi.org/10.1007/BF01254271

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  • DOI: https://doi.org/10.1007/BF01254271

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