On optimal estimators of shift population density functions and conditions of their consistency |
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Authors: | P N Sapozhnikov |
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Institution: | (1) Perm State University, Bukireva, 15, 614600 Perm, Russia |
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Abstract: | A new technique of optimal estimation of density functions for exponential shift families on a homogeneous space of a Lie
group is proposed. In contrast to traditional methods, the approach considered is essentially based on the algebraic properties
of shift families. Here we give a universal formula for consistent estimators of density functions covering different classes
of estimators such as unbiased estimators with uniformly minimum variance and Bayesian estimators under two popular loss functions.
The representations of some maximal invariant density functions are derived and simultaneously a close connection between
the estimators and these density functions is established.
Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part III. |
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Keywords: | |
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