Summary
We consider a semi-Markov chain, with a finite state space. Taking a censored history, we obtain empirical estimators for the discrete semi-Markov kernel, renewal function and semi-Markov transition function. We propose estimators for two different failure rate functions: the usual failure rate, BMP-failure rate, defined by [BMP63], and the new introduced failure rate, RG-failure rate, proposed by [RG92]. We study the strong consistency and the asymptotic normality for each estimator and we construct the confidence intervals. We illustrate our results by a numerical example.
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Barbu, V., Limnios, N. (2006). Nonparametric Estimation for Failure Rate Functions of Discrete Time semi-Markov Processes. In: Nikulin, M., Commenges, D., Huber, C. (eds) Probability, Statistics and Modelling in Public Health. Springer, Boston, MA. https://doi.org/10.1007/0-387-26023-4_5
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DOI: https://doi.org/10.1007/0-387-26023-4_5
Publisher Name: Springer, Boston, MA
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