A0201
Title: A further study on Chen-Qin's test for two-sample Behrens-Fisher problems for high-dimensional data
Authors: Tianming Zhu - National Institute of Education, Nanyang Technological University (Singapore) [presenting]
Jin-Ting Zhang - National University of Singapore (Singapore)
Abstract: A further study on Chen-Qin's test, namely CQ-test, for two-sample Behrens-Fisher problems for high-dimensional data is conducted, resulting in a new normal-reference test where the null distribution of the CQ-test statistic is approximated with that of a chi-squared-type mixture, which is obtained from the CQ-test statistic when the null hypothesis holds and when the two samples are normally distributed. The distribution of the chi-squared-type mixture can be well approximated by a three-cumulant matched chi-squared approximation with the approximation parameters consistently estimated from the data. The asymptotical power of the new normal-reference test under a local alternative is established. Two simulation studies demonstrate that in terms of size control, the new normal-reference test with the three-cumulant matched chi-squared-approximation performs well regardless of whether the data are nearly uncorrelated, moderately correlated, or highly correlated, and it performs substantially better than the CQ-test. A real data example illustrates the new normal-reference test.
