A High-dimensional Test Of Two Population Mean Vectors Based On The Projection

Statistical hypothesis test for high-dimensional data has been an interesting and more difficult problem in recent statistical inference.When the dimension of mean vector is fixed,the well-known Hotelling T² test is,usually applied to test whether two mean vectors are equal or not.However,when the dimension of mean vector is divergent and greater than sample size,the Hotelling T² test is no longer available.In this article,we propose a novel two-population mean vectors test based on projection for the high dimensional data.The proposed test statistic is defined as follows:Tnew=?X₁-X₂?2+kn?a'?X₂-X₂??2;Where kn goes to infinity and a is a known unit vector in Rp.The second component of the proposed test statistic refers to the idea of projection,which improves the test power performance.This proposed test statistic can be adapted to various p>n scenarios,because it does not depend on any inverse matrix.We show that the proposed test statistic has asymptotically standard normal after standardizing under common conditions.Compared with Bai and Saranadasa?1996?^[5]?abbreviated BS?and Chen and Qin?2010?^[2]?abbreviated CQ?,the proposed test statistic enjoys a more significant efficiency power under the local alternative hypothesis.A thorough simulation results show that the proposed test method has a more powerful performance.We further illustrate its application by a significant test of "Sell in May effect in 12 sectors in China A stock market from May 2000 to October 2017.We report that the"Sell in May effect is significant in 7 out of 12 sectors.That is,the stocks monthly returns vector in the November-April period is not equal to that in the May-October period.