A multidimensional functional central limit theorem for an empirical estimator of a continuous-time semi-Markov kernel

S. Georgiadis and N. Limnios

Journal of Nonparametric Statistics, 2012, vol. 24, issue 4, 1007-1017

Abstract: In this article, we consider the empirical estimator of the kernel of a semi-Markov process on continuous time with finite state space. We obtain a functional central limit theorem for this estimator in multidimensional form. Next, we present the corresponding theorem for the empirical estimator of the conditional sojourn-time distribution function. The proofs of our results are based on semi-martingales.

Date: 2012
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DOI: 10.1080/10485252.2012.715162

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