NONPARAMETRIC-ESTIMATION OF SURVIVAL FUNCTIONS FOR DOUBLY CENSORED OBSERVATIONS WHEN THE LIFETIME HAZARD RATE IS PROPORTIONALLY RELATED TO THE CENSORING HAZARD RATES

Let T, X and Y be non-negative random variables, where T is the time of occurrence of an event of interest, X and Y being the left and right censoring variables respectively. In this paper we propose a nonparametric estimator of the survival function, S(T), when T, X and Y are supposed to be independent and their corresponding hazard rates are proportionally related. In this way, our results extend Ebrahimi's work (1985) to the doubly censored data case.