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We provide a semi-parametric analysis for the proportional likelihood ratiomodel, proposed by Luo & Tsai (2012). We study the tangent spaces for both theparameter of interest and the nuisance parameter, and obtain an explicitexpression for the efficient score function. We propose a family ofZ-estimators based on the score functions, including an approximated efficientestimator. Using inverse probability weighting, the proposed estimators canalso be applied to different missing-data mechanisms, such as right censoreddata and non-random sampling. A simulation study that illustrates thefinite-sample performance of the estimators is presented.

Semiparametric Analysis of the Proportional Likelihood Ratio Model and Omnibus Estimation Procedure