A high dimensional dissimilarity measure

A new dissimilarity measure for high-dimensional, low sample size settings to compare high dimensional probability distributions is proposed. The asymptotic behavior of the new dissimilarity index is studied theoretically. Numerical experiments from high dimensional distributions exhibit the usefulness of the method. The eigenvalues of the matrix of dissimilarities for comparing two high dimensional samples are determined and shown to be related to the asymptotic value of the dissimilarity index. A dissimilarity visualization plot that is useful for detection of outliers and change points is proposed and utilized to find the change points in S&P500 stock return data. (c) 2022 Elsevier B.V. All rights reserved.