Estimation of Survival Function Under Random Censorship

Abstract

The paper deals with the estimation of survival function of a particular random variable of interest in proportional hazard model of random censorship under the condition that data are randomly censored by k independent variables. Estimators are constructed using results from Abdushukurov (1984), Cheng and Lin (1984), Ebrahimi (1985) and Kaplan and Meier (1958). The asymptotic behaviour of all these estimators is investigated. Numerical results are provided to calculate the efficiencies of ACL and Ebrahimi's estimators in comparsion to classical Kaplan-Meier (1958) estimator.

The Paradoxical Nature of The Proportional Hazards Model of Random Censorship

“…the corresponding remarks in ). The literature on various aspects of estimation and testing in the proportional hazards submodel and its slight extensions or variants has become quite sizable following 1988; see, for example, Csorgo and Mielniczuk (1988); Ghorai (1989Ghorai ( a, b, 1991; Gijbels and Veraverbeke (1989); Hollander and Peiia (1989); Dikta and Ghorai (1990); Mi (1990); Gijbels and Klonias (1991); Rao and Talwalker (1991); Pattanaik (1991, 1993); Beirlant, Carbonez and van der Meulen (1992); Dhar (1992); Herbst (1992Herbst ( a, b, 1993Herbst ( , 1994; Janssen and Veraverbeke (1992); Stute (1992); Peiia and Rohatgi (1993); Veraverbeke (1994) and Dikta (1995). (A referee has pointed out to us that part of Mi (1990) is incorrect; indeed, all the statements in the paper concerning asymptotic distributions are in error).…”