Asymptotic Efficiency in Censored Alternating Renewal Processes

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 stationarity. 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 when ignoring the stationarity structure in the estimation