In this article, we consider the problem of testing the equality of mean vectors of dimension p of several groups with a common unknown non-singular covariance matrix Σ, based on N independent observation vectors where N may be less than the dimension p. This problem, known in the literature as...

Distance correlation is extended to the problem of testing the independence of random vectors in high dimension. Distance correlation characterizes independence and determines a test of multivariate independence for random vectors in arbitrary dimension. In this work, a modified distance...

Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most loadings are zero. We study the asymptotic properties of these...

The problem of classifying a new observation vector into one of the two known groups distributed as multivariate normal with common covariance matrix is considered. In this paper, we handle the situation that the dimension, p, of the observation vectors is less than the total number, N, of...