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

## TL;DR

This paper conducts a semi-parametric analysis of the proportional likelihood ratio model, deriving efficient score functions and proposing estimators applicable to various missing-data scenarios, supported by simulation results.

## Contribution

It introduces a family of Z-estimators, including an efficient one, for the proportional likelihood ratio model, with applicability to missing data mechanisms.

## Key findings

- Proposed estimators perform well in finite samples.
- Explicit efficient score functions derived for the model.
- Estimators applicable to censored and non-random sampling data.

## 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.