Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

   
 

 

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


Author: O. A. Voĭna
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 85 (2011).
Journal: Theor. Probability and Math. Statist. 85 (2012), 41-52
MSC (2010): Primary 62M05; Secondary 60J99, 93E11
Published electronically: January 11, 2013
MathSciNet review: 2933701
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.


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Additional Information

O. A. Voĭna
Affiliation: Department of Economics and Management, Koszalin University of Technology, E. Kwiatkowskiego Street, 6E, Koszalin, 75-343, Poland
Email: avoina@hotmail.com

DOI: http://dx.doi.org/10.1090/S0094-9000-2013-00872-2
Keywords: Compound Poisson process, incomplete observations, nonparametric estimation, hidden Markov model, Cox model
Received by editor(s): September 9, 2010
Published electronically: January 11, 2013
Article copyright: © Copyright 2013 American Mathematical Society