A rank estimator in the two-sample transformation model with randomly censored data |
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| Authors: | Hideatsu Tsukahara |
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| Affiliation: | (1) Faculty of Economics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, 113 Tokyo, Japan;(2) Present address: Department of Statistics, University of Illinois at Urbana-Champaign, 101 Illini Hall, 725 South Wright Street, 61820 Champaign, IL, U.S.A. |
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| Abstract: | We consider the transformation model which is a generalization of Lehmann alternatives model. This model contains a parameter  and a nonparametric part F1 which is a distribution function. We propose a kind of M-estimator of based on ranks in the presence of random censoring. It is nonparametric in the sense that we do not have to know F1. 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 . We also make a comparison between our estimator and other proposed estimators with real data. |
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| Keywords: | Transformation models M-estimator based on ranks proportional hazards model censored data product-limit estimator empirical processes |
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