Stable convergence of the log-likelihood ratio to a mixture of infinitely divisible distributions |
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Authors: | A F Taraskin |
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Institution: | (1) Department of Technical Cybernetics, Samara State Airspace University, Moskovskoye shosse, 34, 443086 Samara, Russia |
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Abstract: | Some results concerning the asymptotic behavior of the log-likelihood ratio (LLR) and also of certain other random variables
closely associated with the likelihood ratio are presented. More specifically, in the present paper we formulate the conditions
for the stable convergence in distribution of the LLR for two sequences of the probability measures to a mixture of infinitely
divisible distributions with finite variance. Moreover, the notion of a locally asymptotically mixed infinitely divisible
(LAMID) sequence of parametric families of the probability measures is introduced, and it is shown that when a certain kind
of differentiability-type regularity condition is satisfied, the given sequence of families satisfies the LAMID condition.
These results extend and supplement the previous investigations of the author concerning non-Gaussian asymptotic distributions
in statistics.
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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