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On a functional equation appearing in characterization of distributions by the optimality of an estimate

Abstract : Let X be a second countable locally compact Abelian group containing no subgroup topologically isomorphic to the circle group T. Let (\mu_\theta) be a family of probability laws. An optimal estimate of the parameter \theta exists iff the characteristic function of \mu verifies a functional equation. We solve this equation: \mu is a convolution of a Gaussian distribution and a distribution supported in the subgroup of X generated by elements of order 2.
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https://hal.archives-ouvertes.fr/hal-00865938
Contributor : Piotr Graczyk <>
Submitted on : Wednesday, September 25, 2013 - 1:52:08 PM
Last modification on : Monday, March 9, 2020 - 6:15:53 PM
Document(s) archivé(s) le : Friday, April 7, 2017 - 2:41:06 AM

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  • HAL Id : hal-00865938, version 1

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G.M. Feldman, Piotr Graczyk. On a functional equation appearing in characterization of distributions by the optimality of an estimate. 2013. ⟨hal-00865938⟩

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