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Teoriya Veroyatnostei i ee Primeneniya, 1974, Volume 19, Issue 2, Pages 340–354
(Mi tvp2855)
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This article is cited in 2 scientific papers (total in 2 papers)
On the behaviour of the generalized Вayes estimates for Markov observations
B. Ya. Levit Moscow
Abstract:
We consider the behaviour of the generalized Bayes estimates $\widehat\theta_n$ of an unknown parameter $\theta$ assuming that the observations $X_1,\dots,X_n,\dots$ form a transient Markov chain. It is shown that, under some conditions, the limit distribution of the sequence $\sqrt n(\widehat\theta_n-\theta)$ is a weighted normal law. The main restriction is that there must exist a.s. nonzero limit of the $I(X_n)$, where $I(X)$ is the (conditioned) Fiser information. Some examples show that, if this restriction is not satisfied, the estimation problem becomes “irregular”.
Received: 03.08.1971
Citation:
B. Ya. Levit, “On the behaviour of the generalized Вayes estimates for Markov observations”, Teor. Veroyatnost. i Primenen., 19:2 (1974), 340–354; Theory Probab. Appl., 19:2 (1975), 332–346
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Abstract page: | 145 | Full-text PDF : | 76 |
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