Semiparametric Models and Likelihood - The Power of Ranks

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”.