Title: On simultaneous confidence interval estimation for the difference of paired mean vectors in high-dimensional settings
Authors: Masashi Hyodo - Osaka Prefecture University (Japan) [presenting]
Hiroki Watanabe - Tokyo University of Science (Japan)
Abstract: To test whether two populations have the same mean vector in a high-dimensional setting, an unbiased estimator of the squared Euclidean distance between the mean vectors has been previously derived, and the asymptotic normality of this estimator has been proved under local assumptions about the mean vectors. These results are extended without assumptions about the mean vectors. In addition, asymptotic normality is established in a class of general statistics which includes important statistics under general moment conditions that cover both the previous moment condition and elliptical distributional assumption. These asymptotic results are applied to the construction of simultaneous intervals for all pair-wise differences between mean vectors of $k>2$ groups. The finite-sample and dimension performance of the proposed methods is also studied via Monte Carlo simulations. The methodology is illustrated using microarray data.