INFORMATION AND ASYMPTOTIC EFFICIENCY IN SOME GENERALIZED PROPORTIONAL HAZARDS MODELS FOR COUNTING-PROCESSES

Proportional hazards models with stochastic baseline hazards and estim ators of the relative risk coefficient in these models were proposed b y Prentice, Williams and Peterson and by Chang and Hsiung in medical a nd industrial contexts. The form of the estimating functions recommend ed varies according to the form of the unknown stochastic baseline haz ards. This paper examines the same estimation problem in the context o f large-sample theory. It is shown that the proposed estimators are re gular, asymptotically normal and asmptotically efficient. Asymptotic i nformation and representation theorems in the sense of Begun, Hall, Hu ang and Wellner are also provided for these models.