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2021 Empirical likelihood ratio test on quantiles under a density ratio model
Archer Gong Zhang, Guangyu Zhu, Jiahua Chen
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Electron. J. Statist. 15(2): 6191-6227 (2021). DOI: 10.1214/21-EJS1943

Abstract

Population quantiles are important parameters in many applications. Enthusiasm for the development of effective statistical inference procedures for quantiles and their functions has been high for the past decade. In this article, we study inference methods for quantiles when multiple samples from linked populations are available. The research problems we consider have a wide range of applications. For example, to study the evolution of the economic status of a country, economists monitor changes in the quantiles of annual household incomes, based on multiple survey datasets collected annually. Even with multiple samples, a routine approach would estimate the quantiles of different populations separately. Such approaches ignore the fact that these populations are linked and share some intrinsic latent structure. Recently, many researchers have advocated the use of the density ratio model (DRM) to account for this latent structure and have developed more efficient procedures based on pooled data. The nonparametric empirical likelihood (EL) is subsequently employed. Interestingly, there has been no discussion in this context of the EL-based likelihood ratio test (ELRT) for population quantiles. We explore the use of the ELRT for hypotheses concerning quantiles and confidence regions under the DRM. We show that the ELRT statistic has a chi-square limiting distribution under the null hypothesis. Simulation experiments show that the chi-square distributions approximate the finite-sample distributions well and lead to accurate tests and confidence regions. The DRM helps to improve statistical efficiency. We also give a real-data example to illustrate the efficiency of the proposed method.

Acknowledgments

The authors are grateful to the referees and the Editor for their helpful comments and suggestions.

Citation

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Archer Gong Zhang. Guangyu Zhu. Jiahua Chen. "Empirical likelihood ratio test on quantiles under a density ratio model." Electron. J. Statist. 15 (2) 6191 - 6227, 2021. https://doi.org/10.1214/21-EJS1943

Information

Received: 1 December 2020; Published: 2021
First available in Project Euclid: 27 December 2021

Digital Object Identifier: 10.1214/21-EJS1943

Subjects:
Primary: 62G20
Secondary: 62G10 , 62G15

Keywords: confidence region , density ratio model , empirical likelihood , likelihood ratio test , multiple samples , Quantile estimation

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Vol.15 • No. 2 • 2021
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