Seminar| Institute of Mathematical Sciences
Time: Friday, March 15th, 2024 , 16:00-17:00
Abstract: We propose a promising high-dimensional two-sample mean test method, the DCF test, which makes broader assumptions than traditional methods about the moments and tails of the elements in random vectors, without imposing too many constraints on the distribution and correlation structure of individuals in the samples. Specifically, this method allows for any distribution type of individuals in the samples (e.g., not limited to independent and identically distributed or sub-Gaussian distributions) and any correlation structure among individual samples (e.g., correlation matrices don't have to be invertible or eigenvalues bounded). Further desired features include allowance for highly unequal sample sizes, consistent power behavior under fairly general alternative, data dimension allowed to be exponentially high under the umbrella of such general conditions. In terms of application, by comparing this test with many traditional testing methods through simulation experiments and real data analysis, the DCF test has shown relative superiority in various complex application scenarios, thereby further validating the effectiveness of the related theories.