Two-sample high-dimensional empirical likelihood

Jianglin Fang, Wanrong Liu and Xuewen Lu

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 13, 6323-6335

Abstract: In this paper, we apply empirical likelihood for two-sample problems with growing high dimensionality. Our results are demonstrated for constructing confidence regions for the difference of the means of two p-dimensional samples and the difference in value between coefficients of two p-dimensional sample linear model. We show that empirical likelihood based estimator has the efficient property. That is, as p → ∞ for high-dimensional data, the limit distribution of the EL ratio statistic for the difference of the means of two samples and the difference in value between coefficients of two-sample linear model is asymptotic normal distribution. Furthermore, empirical likelihood (EL) gives efficient estimator for regression coefficients in linear models, and can be as efficient as a parametric approach. The performance of the proposed method is illustrated via numerical simulations.

Date: 2017
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DOI: 10.1080/03610926.2015.1115072

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