Abstract
We consider a two-sample semiparametric model involving a real parameter θ and a nuisance parameter F which is a distribution function. This model includes the proportional hazard, proportional odds, linear transformation and Harrington-Fleming models (1982, Biometrika, 69, 533–546). We propose two types of estimates based on ranks. The first is a rank approximation to Huber's M-estimates (1981, Robust Statistics, Wiley) and the second is a Hodges-Lehmann type rank inversion estimate (1963, Ann. Math. Statist., 34, 598–611). We obtain asymptotic normality and efficiency results. The estimates are consistent and asymptotically normal generally but fully efficient only for special cases.
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Research partially supported by National Science Foundation Grant DMS-86-02083 and National Institute of General Medical Sciences Grant SSS-Y1RO1GM35416-01
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Dabrowska, D.M., Doksum, K.A. & Miura, R. Rank estimates in a class of semiparametric two-sample models. Ann Inst Stat Math 41, 63–79 (1989). https://doi.org/10.1007/BF00049110
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DOI: https://doi.org/10.1007/BF00049110