A RANK ESTIMATOR IN THE TWO-SAMPLE TRANSFORMATION MODEL WITH RANDOMLY CENSORED DATA

HIDEATSU TSUKAHARA

Faculty of Economics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan

(Received November 1, 1990; revised April 15, 1991)

Abstract. We consider the transformation model which is a generalization of Lehmann alternatives model. This model contains a parameter θ and a nonparametric part F_{1} which is a distribution function. We propose a kind of M -estimator of θ based on ranks in the presence of random censoring. It is nonparametric in the sense that we do not have to know F_{1}. Moreover, it is simple and asymptotically normal. For the proportional hazards model with special censoring, we obtain the asymptotic relative efficiency of our estimator with respect to the best nonparametric estimator for this model. It is quite efficient for special values of θ. We also make a comparison between our estimator and other proposed estimators with real data.

Key words and phrases: Transformation models, M -estimator based on ranks, proportional hazards model, censored data, product-limit estimator, empirical processes.