Maximum likelihood estimation in alternating renewal processes under window censoring

Abstract

Consider a process that jumps back and forth between two states, with random times spent in between. Suppose the durations of subsequent on and off states are i.i.d. and that the process has started far in the past, so it has achieved stasis. We estimate the sojourn distributions through maximum likelihood when data consist of several realizations observed over windows of fixed length. For discrete and continuous time Markov chains, we also examine if there is any loss of efficiency incurred when ignoring the stationarity structure in the estimation.