ON LIKELIHOOD ESTIMATION FOR DISCRETELY OBSERVED MARKOV JUMP PROCESSES

ON LIKELIHOOD ESTIMATION FOR DISCRETELY OBSERVED MARKOV JUMP PROCESSES

Summary The parameter estimation problem for a Markov jump process sampled at equidistant time points is considered here. Unlike the diffusion case where a closed form of the likelihood function is usually unavailable, here an explicit expansion of the likelihood function of the sampled chain is pro...

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Veröffentlicht in:Australian & New Zealand journal of statistics 2007-03, Vol.49 (1), p.93-107
Hauptverfasser: Dehay, Dominique, Yao, Jian-Feng
Format: Artikel
Sprache:eng
Schlagworte:
discrete observations
likelihood estimator
Markov jump process
Mathematics
Statistics
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container_title Australian & New Zealand journal of statistics
container_volume 49
creator Dehay, Dominique
Yao, Jian-Feng
description Summary The parameter estimation problem for a Markov jump process sampled at equidistant time points is considered here. Unlike the diffusion case where a closed form of the likelihood function is usually unavailable, here an explicit expansion of the likelihood function of the sampled chain is provided. Under suitable ergodicity conditions on the jump process, the consistency and the asymptotic normality of the likelihood estimator are established as the observation period tends to infinity. Simulation experiments are conducted to demonstrate the computational facility of the method.
doi_str_mv 10.1111/j.1467-842X.2006.00466.x
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subjects discrete observations
likelihood estimator
Markov jump process
Mathematics
Statistics
title ON LIKELIHOOD ESTIMATION FOR DISCRETELY OBSERVED MARKOV JUMP PROCESSES
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