Testing the Equality of High Dimensional Distributions

Music City Center 

A fast and powerful method for comparing and visualizing high-dimensional
datasets is presented. A novel statistic that is inspired by the interpoint
distances, but avoids their computation is proposed. The Euclidean distance
is not a suitable distance for high dimensional settings due to the distance
concentration phenomenon. We offer statistics based on two high-dimensional
dissimilarity indices that take advantage of the concentration phenomenon.
A simultaneous display of observations means and standard deviations that aids visualization,
detection of suspect outliers, and enhances separability among the competing classes in
the transformed space is discussed. We study the finite sample convergence of the dissimilarity indices,
compare eight statistics under several distributions, and present three applications.

Interpoint distance;

Concentration;

Dissimilarity Indices. 

Section on Nonparametric Statistics