Nonparametric estimation for a compound Poisson process governed by a Markov chain
Author:
O. A. Voĭna
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 85 (2012), 41-52
MSC (2010):
Primary 62M05; Secondary 60J99, 93E11
DOI:
https://doi.org/10.1090/S0094-9000-2013-00872-2
Published electronically:
January 11, 2013
MathSciNet review:
2933701
Full-text PDF Free Access
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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.
References
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- A. A. Voĭna and E. Czapla, An application of the correlation structure of a Markov chain for the estimation of shift parameters in queuing systems, Teor. Imovir. Mat. Stat. v71 (2004), 49–56; English transl. in Theor. Prob. Math. Statist. 71 (2005), 53–61.
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References
- V. V. Anisimov, Random Processes with a Discrete Component. Limit Theorems, “Vyshcha Shkola”, Kiev, 1988. (Russian) MR 955492 (89m:60003)
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- I. I. Gikhman and A. V. Skorokhod, The Theory of Stochastic Processes, vol. 1, “Nauka”, Moscow, 1971; vol. 2, “Nauka”, Moscow, 1973; English transl., vol. 1, Springer-Verlag, New York–Heidelberg, 1974; vol. 2, Springer-Verlag, New York–Heidelberg, 1975.
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- A. A. Voĭna and E. Czapla, An application of the correlation structure of a Markov chain for the estimation of shift parameters in queuing systems, Teor. Imovir. Mat. Stat. v71 (2004), 49–56; English transl. in Theor. Prob. Math. Statist. 71 (2005), 53–61.
- A. Wojna, Ryzyko w Procesach Finansowych Oraz Metody Badania Koniunktury, PK, Koszalin, 2009.
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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
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
