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June 2013 Quantile and quantile-function estimations under density ratio model
Jiahua Chen, Yukun Liu
Ann. Statist. 41(3): 1669-1692 (June 2013). DOI: 10.1214/13-AOS1129


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.


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Jiahua Chen. Yukun Liu. "Quantile and quantile-function estimations under density ratio model." Ann. Statist. 41 (3) 1669 - 1692, June 2013.


Published: June 2013
First available in Project Euclid: 1 August 2013

zbMATH: 1292.62072
MathSciNet: MR3113825
Digital Object Identifier: 10.1214/13-AOS1129

Primary: 62G20
Secondary: 62G15

Keywords: Asympotic efficiency , Bahadur representation , Confidence interval , empirical likelihood

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 3 • June 2013
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