QUANTILE AND QUANTILE-FUNCTION ESTIMATIONS UNDER DENSITY RATIO MODEL1

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 es-timators are shown to admit a Bahadur representation that leads to asymp-totically valid confidence intervals for functions of quantiles. We rigorously prove that EL quantiles based on all the samples are more efficient than empir-ical 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 exam-ple is used to demonstrate the new method and the potential cost savings