On the asymptotic properties of some kernel estimators for continuous-time semi-Markov processes

Chafiâa Ayhar, Vlad Stefan Barbu, Fatiha Mokhtari and Saâdia Rahmani

Journal of Nonparametric Statistics, 2022, vol. 34, issue 2, 299-318

Abstract: This paper provides kernel estimators of the main characteristics of a continuous-time semi-Markov process, like conditional and unconditional sojourn times in a state, semi-Markov kernel, etc. The main goal of this paper is to establish asymptotic properties of the semi-Markov kernel estimators and of the sojourn time distribution estimators (conditional and unconditional), as well as of the estimators of the associated Radon-Nikodym derivatives, when the sample size becomes large. The approach is illustrated by considering a three state example with detailed calculus and numerical evaluations.

Date: 2022
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DOI: 10.1080/10485252.2022.2044033

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