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.
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Tsukahara, H. A rank estimator in the two-sample transformation model with randomly censored data. Ann Inst Stat Math 44, 313–333 (1992). https://doi.org/10.1007/BF00058643
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DOI: https://doi.org/10.1007/BF00058643