Information and Asymptotic Efficiency in Some Generalized Proportional Hazards Models for Counting Processes

Abstract

Proportional hazards models with stochastic baseline hazards and estimators of the relative risk coefficient in these models were proposed by Prentice, Williams and Peterson and by Chang and Hsiung in medical and industrial contexts. The form of the estimating functions recommended varies according to the form of the unknown stochastic baseline hazards. This paper examines the same estimation problem in the context of large-sample theory. It is shown that the proposed estimators are regular, asymptotically normal and asymptotically efficient. Asymptotic information and representation theorems in the sense of Begun, Hall, Huang and Wellner are also provided for these models.