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Distribution-Free Multisample Test Based on Optimal Matching with Applications to Single Cell Genomics by Agarwal, Divyansh; Mukherjee, Somabha; Bhattacharya, Bhaswar Bikram; Zhang, Nancy Ruonan is a scholarly article available to read on EtoBox.

What is Distribution-Free Multisample Test Based on Optimal Matching with Applications to Single Cell Genomics about?

In this paper we propose a nonparametric graphical test based on optimal matching, for assessing the equality of multiple unknown multivariate probability distributions. Our procedure pools the data from the different classes to create a graph based on the minimum non-bipartite matching, and then utilizes the number of edges connecting data points from different classes to examine the closeness between the distributions. The proposed test is exactly distribution-free (the null distribution does not depend on the distribution of the data) and can be efficiently applied to multivariate as well as non-Euclidean data, whenever the inter-point distances are well-defined. We show that the test is universally consistent, and prove a distributional limit theorem for the test statistic under general alternatives. Through simulation studies, we demonstrate its superior performance against other common and well-known multisample tests. In scenarios where our test suggests distributional differences across classes, we also propose an approach for identifying which class or group contributes to this overall difference. The method is applied to single cell transcriptomics data obtained from the

Author

Agarwal, Divyansh; Mukherjee, Somabha; Bhattacharya, Bhaswar Bikram; Zhang, Nancy Ruonan

Published

2019

Language

EN