Stable convergence of the log-likelihood ratio to a mixture of infinitely divisible distributions (Q1368804)
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scientific article; zbMATH DE number 1068215
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stable convergence of the log-likelihood ratio to a mixture of infinitely divisible distributions |
scientific article; zbMATH DE number 1068215 |
Statements
Stable convergence of the log-likelihood ratio to a mixture of infinitely divisible distributions (English)
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2 December 1998
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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. The author formulates conditions for stable convergence in distribution of the LLR for two sequences of 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 probability measures is introduced. It is shown that under a certain kind of differentiability-type regularity condition a given sequence of families satisfies the LAMID condition.
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log-likelihood ratio
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locally asymptotically mixed normal
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stable convergence
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