On some graph-based two-sample tests for high dimension, low sample size data

Soham Sarkar
SPRINGER, 2020
Journal paper

Testing for equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been proposed in the literature, which can be used for data of arbitrary dimensions. Most of these test statistics are computed using pairwise Euclidean distances among the observations. But, due to concentration of pairwise Euclidean distances, these tests have poor performance in many high-dimensional problems. Some of them can have powers even below the nominal level when the scale-difference between two distributions dominates the location-difference. To overcome these limitations, we introduce some new dissimilarity indices and use them to modify some popular graph-based tests. These modified tests use the distance concentration phenomenon to their advantage, and as a result, they outperform the corresponding tests based on the Euclidean distance in a wide variety of examples. We establish the high-dimensional consistency of these modified tests under fairly general conditions. Analyzing several simulated as well as real data sets, we demonstrate their usefulness in high dimension, low sample size situations.

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Soham Sarkar
SPRINGER, 2020
Journal paper

Abstract

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https://infoscience.epfl.ch/record/272769?ln=en

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Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a d

Data set

A data set (or dataset) is a collection of data. In the case of tabular data, a data set corresponds to one or more database tables, where every column of a table represents a particular variable, an

Sample size determination

Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which th