A semiparametric shock model for a pair of event-related dependent censored failure times

To derive our results, we define a joint distribution for the pair of failure times by means of a pair of parameters and a pair of baseline hazard rates. We then construct the associated counting processes and their compensators: in particular, we exhibit a special form of the risk indicators. We then propose a maximal partial likelihood estimator for the pair of parameters and Breslow estimators for the pair of baseline cumulative hazard rates. We establish the large sample properties of our estimators, following Andersen et al. [1993. Statistical Models based on Counting Processes. Springer, New York] and we illustrate our results by a short simulation study and an application to a real data set in demography.