This article is cited 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

 English version: Theory of Probability and its Applications, 1975, 19:2, 332–346

Bibliographic databases:

• 
•