Two-sample high-dimensional empirical likelihood. Issue 13 (3rd July 2017)

• Record Type: Journal Article
• Authors: Fang, Jianglin; Liu, Wanrong; Lu, Xuewen
• Is Part Of: Communications in statistics. Volume 46:Issue 13(2017)
• Page Start: 6323
• Page End: 6335
• Publication Date: 2017-07-03
• Subjects: Confidence region -- empirical likelihood -- high-dimensional data analysis -- linear model -- two-sample problem.; 62G20 -- 62H15; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2015.1115072
• Languages: English
• ISSNs: 0361-0926

Abstract

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.