Nonparametric estimation for a compound Poisson process governed by a Markov chain

The problem of nonparametric estimation for a Poisson process governed by a Markov chain with continuous time is considered in the case of incomplete observations. A method of the nonparametric estimation is proposed. The method is based on a representation of such a process in the form of a hidden...

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Bibliographic Details
Published in:Theory of probability and mathematical statistics 2012, Vol.85, p.41-52
Main Author: O. A. Voĭna
Format: Article
Language:English
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Summary:The problem of nonparametric estimation for a Poisson process governed by a Markov chain with continuous time is considered in the case of incomplete observations. A method of the nonparametric estimation is proposed. The method is based on a representation of such a process in the form of a hidden Markov model. An example for the estimation of unknown distribution functions is considered in the case of incomplete observations after a compound Poisson process governed by a simple Markov regenerative process.
ISSN:0094-9000
1547-7363
DOI:10.1090/S0094-9000-2013-00872-2