Empirical likelihood test for a large-dimensional mean vector
成果类型：
Article
署名作者：
Cui, Xia; Li, Runze; Yang, Guangren; Zhou, Wang
署名单位：
Guangzhou University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Jinan University; National University of Singapore
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asaa005
发表日期：
2020
页码：
591607
关键词：
摘要：
This paper is concerned with empirical likelihood inference on the population mean when the dimension p and the sample size n satisfy p/n -> c is an element of [1, infinity). As shown in Tsao (2004), the empirical likelihood method fails with high probability when p/n > 1/2 because the convex hull of the n observations in R-p becomes too small to cover the true mean value. Moreover, when p > n, the sample covariance matrix becomes singular, and this results in the breakdown of the first sandwich approximation for the log empirical likelihood ratio. To deal with these two challenges, we propose a newstrategy of adding two artificial data points to the observed data. We establish the asymptotic normality of the proposed empirical likelihood ratio test. The proposed test statistic does not involve the inverse of the sample covariance matrix. Furthermore, its form is explicit, so the test can easily be carried out with low computational cost. Our numerical comparison shows that the proposed test outperforms some existing tests for high-dimensional mean vectors in terms of power. We also illustrate the proposed procedure with an empirical analysis of stock data.