Semi-parametric estimation for a semi-Markov process with left-truncated and right-censored observations

A semi-Markov process is characterized by the transition probabilities between the states and the distribution functions of the duration times between the occurrence of consecutive states. We present estimators of the transition probabilities and the cumulative hazard functions of the duration times when n i.i.d. right-censored sample paths of a process are observed, with left-truncated and right-censored sojourn times.