Minimum divergence estimators for the Radon-Nikodym derivatives of the semi-Markov kernel

摘要

In this paper we face the problem of estimating the elements that define a homogeneous semi-Markov process. Given an observed sample path of the process in a finite interval , non-parametric estimators of the entries of the semi-Markov kernel and its derivatives can be constructed. These estimators exhibit good properties as consistency and asymptotic normality. On the other hand, in our approach we consider that we have some prior information about the underlying process. This information concerns the mean sojourn times in the different states of the process and has to be taken into account in the estimation procedure. So we start from the smoothed estimators and construct minimum divergence estimators (maximum entropy) under some constraints for the associated sojourn moments.