Nonparametric Estimation of the Stationary Distribution of a Discrete-Time Semi-Markov Process

Stylianos Georgiadis, Nikolaos Limnios

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this article, we consider a discrete-time semi-Markov process with finite state space and an observation censored at an arbitrary fixed time. Some intermediate results concerning the empirical estimation of the mean recurrence times of the embedded Markov process and the mean sojourn times of the semi-Markov process are given. We study two nonparametric estimators for the stationary distribution of the semi-Markov process and examine their asymptotic properties, such as strong consistency and asymptotic normality, as the length of the observation tends to infinity. Finally, a numerical application is presented to illustrate the comparison of the two estimators.
Original languageEnglish
JournalCommunications in Statistics: Theory and Methods
Volume44
Issue number7
Pages (from-to)1319-1337
ISSN0361-0926
DOIs
Publication statusPublished - 2015
Externally publishedYes

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