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Abstract
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Population quantiles and their functions are important parameters in many applications. For example,the lower level quantiles often serve as crucial quality indices of forestry products and others. In the presence of several independent samples from populations satisfying density ratio model, we investigate the properties of the empirical likelihood (EL) based inferences of quantiles and their functions. In this paper, we first establish the consistency and asymptotic normality of the estimators of parameters and cumulative distributions. The induced EL quantile estimators are then shown to admit Bahadur representation. The results are used to construct asymptotically valid confidence intervals for functions of quantiles. In addition, we rigorously prove that the EL quantiles based on all samples are more efficient than the empirical quantiles which can only utilize information from individualsamples. Simulation study shows that the EL quantiles and their functions have superior performances both when the density ratio model assumption is satisfied and mildly violated. An application example is used to demonstrate the new methods and potential cost savings.
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