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

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.

Keywords:

• Semi-Markov processes
• kernel estimator
• sojourn times
• semi-Markov kernel
• consistency
• asymptotic normality

AMS Subject Classifications:

• Primary: 60G
• 60F
• 62M

Disclosure statement

No potential conflict of interest was reported by the authors.