To test whether two populations have the same mean vector in a high-dimensional setting, Chen and Qin (2010, Ann. Statist.) derived an unbiased estimator of the squared Euclidean distance between the mean vectors and proved the asymptotic normality of this estimator under local assumptions about the mean vectors. In this study, their results are extended without assumptions about the mean vectors. In addition, asymptotic normality is established in the class of general statistics including Chen and Qin's statistics and other important statistics under general moment conditions that cover both Chen and Qin's 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.
- Confidence interval
- High dimension
- Statistical hypothesis testing