Quantile and quantile-function estimations under density ratio model

TL;DR

This paper develops empirical likelihood-based methods for estimating population quantiles under the density ratio model, demonstrating improved efficiency and valid confidence intervals through theoretical proofs and simulations.

Contribution

It introduces EL-based quantile estimators under the density ratio model, proving their asymptotic properties and superior efficiency over traditional methods.

Findings

EL quantiles admit Bahadur representation for valid inference

EL quantiles are more efficient than empirical quantiles

Simulation shows superior performance under the density ratio model

Abstract

Population quantiles and their functions are important parameters in many applications. For example, the lower quantiles often serve as crucial quality indices for forestry products. Given several independent samples from populations satisfying the density ratio model, we investigate the properties of empirical likelihood (EL) based inferences. The induced EL quantile estimators are shown to admit a Bahadur representation that leads to asymptotically valid confidence intervals for functions of quantiles. We rigorously prove that EL quantiles based on all the samples are more efficient than empirical quantiles based on individual samples. A simulation study shows that the EL quantiles and their functions have superior performance when the density ratio model assumption is satisfied and when it is mildly violated. An example is used to demonstrate the new method and the potential cost savings.