Is. Chang et Ca. Hsiung, INFORMATION AND ASYMPTOTIC EFFICIENCY IN SOME GENERALIZED PROPORTIONAL HAZARDS MODELS FOR COUNTING-PROCESSES, Annals of statistics, 22(3), 1994, pp. 1275-1298
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.