TY - JOUR
T1 - Empirical likelihood test for a large-dimensional mean vector
AU - Cui, Xia
AU - Li, Runze
AU - Yang, Guangren
AU - Zhou, Wang
N1 - Funding Information:
The authors thank the editor, associate editor and two reviewers for their constructive comments, as well as Ms A. Applegate for her help with the writing. This work was supported by
Funding Information:
the National Natural Science Foundation of China, the U.S. National Institutes of Health and National Science Foundation, the National Social Science Foundation of China, Fundamental Research Funds for the Central University, and the Ministry of Education Tier One grant at the National University of Singapore.
PY - 2020/9/1
Y1 - 2020/9/1
N2 - This paper is concerned with empirical likelihood inference on the population mean when the dimension p and the sample size n satisfy p/n → cϵ [1,∞). 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 ℝp 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 new strategy 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.
AB - This paper is concerned with empirical likelihood inference on the population mean when the dimension p and the sample size n satisfy p/n → cϵ [1,∞). 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 ℝp 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 new strategy 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.
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U2 - 10.1093/biomet/asaa005
DO - 10.1093/biomet/asaa005
M3 - Article
AN - SCOPUS:85093663663
VL - 107
SP - 591
EP - 607
JO - Biometrika
JF - Biometrika
SN - 0006-3444
IS - 3
ER -