ON SEMIPARAMETRIC INFERENCE FOR MODULATED RENEWAL PROCESSES

Modulated renewal processes, suggested by D. R. Cox, give a flexible w ay to introduce dependencies into point processes. We discuss the asym ptotics of partial likelihood inference for modulated renewal processe s when the random covariate for the process involves its history. We s how, in some generality, that the estimators of the regression paramet er and the cumulative hazard have the same asymptotic distributions th at they would have under the usual proportional hazards model, even th ough the martingale justification for partial likelihood no longer app lies because of a reordering of the time-scale. An example is given to illustrate the ideas. A simulation study is presented to confirm the theoretical results.