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Professor Ming-Yen Cheng is currently Professor at Department of Mathematics of the Hong Kong Baptist University. Her past work experiences include Chair of Statistics at Department of Statistical Science of the University College London (2008-2010) and Distinguished Professor at Department of Mathematics of the National Taiwan University (2006-2008 and 2010-2017). She received her PhD in statistics from the University of North Carolina at Chapel Hill 1994, after finishing her BSc in mathematics and MSc in statistics degrees at the National Tsinghua University in 1988 and 1990. In 1996-1997 she was a postdoctoral fellow at the Australian National University. Her research interests and contributions lies in nonparametric and semiparametric models, high-dimensional data, change-points, classification and clustering, etc. She was elected to Fellow of the Institute of Mathematical Statistics (IMS) in 2007 and Fellow of the American Statistical Association (ASA) in 2009. Her service to the profession include Member of ASA's Board of Directors and Organizing Committee for the International Prize in Statistics, IMS's Committee on Nomination, Committee on Fellows, Committee on Asia Pacific Rim Meetings, and ICSA's Award and Nomination and Election Committees. She is active in editorial service, such as associate editor of Annals of Statistics, Journal of the American Statistical Association and so on, as well as conference organization.

Abstract: Testing the equality of two means is a fundamental inference problem. For high-dimensional data, the Hotelling's T-square test either performs poorly or becomes inapplicable. Several modifications have been proposed to address this issue. However, most of them are based on asymptotic normality of the null distributions of their test statistics which inevitably requires strong assumptions on the covariance matrix. We study this problem thoroughly and propose an L2-norm based test that works under mild conditions and even when there are fewer observations than the dimension. Specifically, to cope with general non-normality of the null distribution we employ the Welch-Satterthwaite chi-square approximation. We derive a sharp upper bound on the approximation error and use it to justify that the chi-square approximation is preferred to normal approximation. Simple ratio-consistent estimators for the parameters in the chi-square approximation are given. Importantly, our test can cope with singularity or near singularity of the unknown covariance which is commonly seen in high dimensions and is the main cause of non-normality. The power of the proposed test is also investigated. Extensive simulation studies and an application show that our test outperforms several existing tests in terms of size control, and the powers are comparable when their sizes are comparable.