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.
Domains
Probability [math.PR]
Origin : Files produced by the author(s)
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