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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Abstract

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

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

Dates
First available in Project Euclid: 3 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1249305325

Digital Object Identifier
doi:10.1214/09-LNMS5707

Mathematical Reviews number (MathSciNet)
MR2681659

Zentralblatt MATH identifier
1271.62066

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

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

Rights
Copyright © 2009, Institute of Mathematical Statistics

Citation

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. https://projecteuclid.org/euclid.lnms/1249305325


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