B1442
Title: A pairwise Hotelling method for testing high-dimensional mean vectors
Authors: Tiejun Tong - Hong Kong Baptist University (Hong Kong) [presenting]
Abstract: For high-dimensional small sample size data, Hotelling's $T_2$ test is not applicable for testing mean vectors due to the singularity problem in the sample covariance matrix. To overcome the problem, there are three main approaches in the literature. Note, however, that each of the existing approaches may have serious limitations and only works well in certain situations. Inspired by this, a pairwise Hotelling method is proposed for testing high-dimensional mean vectors, which, in essence, provides a good balance between the existing approaches. To effectively utilize the correlation information, the new test statistics are constructed as the summation of Hotelling's test statistics for the covariate pairs with strong correlations and the squared t statistics for the individual covariates that have little correlation with others. The asymptotic null distributions and power functions are further derived for the proposed Hotelling's tests under some regularity conditions. Numerical results show that the new tests can control the type I error rates and achieve a higher statistical power compared to existing methods, especially when the covariates are highly correlated. Two real data examples are also analyzed, and they both demonstrate the efficacy of our pairwise Hotelling's tests.
