Institute of Mathematical Statistics Lecture Notes - Monograph Series

Semiparametric Models and Likelihood - The Power of Ranks

Kjell Doksum and Akichika Ozeki

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We consider classes of models related to those introduced by Lehmann [Ann. Math. Statist. 24 (1953) 23–43] and Sklar [L’Institut de Statistique de L’Universite de Paris 8 (1959) 229–231]. Recently developed algorithms for finding profile NP likelihood procedures are discussed, extended and implemented for such models by combining them with the MM algorithm. In particular we consider statistical procedures for a regression model with proportional expected hazard rates, and for transformation models including the normal copula. A variety of likelihoods introduced to deal with semiparametric models are considered. They all generate rank results, not only tests, but also estimates, confidence regions, and optimality theory, thereby, to paraphrase Lehmann [Ann. Math. Statist. 24 (1953) 23–43], demonstrating “the power of ranks”.

Chapter information

Javier Rojo, ed., Optimality: The Third Erich L. Lehmann Symposium (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2009), 67-92

First available in Project Euclid: 3 August 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G20: Asymptotic properties
Secondary: 62N02: Estimation

Lehmann model proportional hazard model profile NP likelihood nonparametric maximum likelihood MM algorithm copula models Box-Cox models

Copyright © 2009, Institute of Mathematical Statistics


Rojo, Javier. Semiparametric Models and Likelihood - The Power of Ranks. Optimality, 67--92, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2009. doi:10.1214/09-LNMS5707.

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