Prof. Runze Li：Empirical likelihood test for a large dimensional mean vector

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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Prof. Runze Li，Penn State University， USA
Inviter:	陈敏研究员
Title:	Empirical likelihood test for a large dimensional mean vector
Time & Venue:	2019.12.23 10:00 N620
Abstract:	This paper is concerned with empirical likelihood inference on the population mean when thedimension p and sample size n satisfy p/n tending to c > =1. As shown in Tsao (2004), the empirical likelihood method fails with high probability when p/n>0.5 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 new strategy of adding two pseudo data points to the observed data. We further 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, thus the proposed test can easily be carried out with low computational cost. Our numerical comparison implies that the proposed test outperforms some existing tests for high dimensional mean vectors in terms of power. We also illustrate the proposed procedure by a real data example.