Soham Sarkar

TL;DR: In this article, the authors point out some limitations of this test and propose some modifications to overcome them retaining its distribution-free property and demonstrate the utility of their proposed modifications on simulated and real data sets.

TL;DR: This article proposes some tests based on ranks of nearest neighbors, which can be conveniently used in high dimension, low sample size situations.

Abstract: Over the last two decades, several two‐sample tests based on averages of inter‐point distances have been proposed in the literature. Most of these tests are based on the Euclidean distance, and they can be used even when the dimension of the data is much larger than the sample size. But these tests can produce poor results in high‐dimensional set‐ups even when the two distributions differ widely in their scatters and shapes. To overcome these limitations, we modify some tests by replacing the Euclidean distance with a new class of distance functions. The high‐dimensional consistency of these modified tests is established under appropriate regularity conditions. Numerical studies are also carried out to demonstrate the usefulness of the proposed methods. Copyright © 2018 John Wiley & Sons, Ltd.

TL;DR: The proposed classifier can be conveniently used even when the dimension is larger than the sample size, and its good discriminatory power for such data has been established using theoretical as well as numerical results.