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

Abstract

We provide a semi-parametric analysis for the proportional likelihood ratio model, proposed by Luo & Tsai (2012). We study the tangent spaces for both the parameter of interest and the nuisance parameter, and obtain an explicit expression for the efficient score function. We propose a family of Z-estimators based on the score functions, including an approximated efficient estimator. Using inverse probability weighting, the proposed estimators can also be applied to different missing-data mechanisms, such as right censored data and non-random sampling. A simulation study that illustrates the finite-sample performance of the estimators is presented.

arXiv commentThe paper includes a correction to an error in the proof of Theorem 3. It also discusses the connection between the model of Luo & Tsai (2012) and the proportional odds model discussed by Liang and Qin (2000), Chen (2003,2007), and Tchetgen Tchetgen et al.(2010)