Nonparametric K-Sample Tests via Dynamic Slicing

Abstract

K-sample testing problems arise in many scientific applications and have attracted statisticians’ attention for many years. We propose an omnibus nonparametric method based on an optimal discretization (aka “slicing”) of continuous random variables in the test. The novelty of our approach lies in the inclusion of a term penalizing the number of slices (i.e., the resolution of the discretization) so as to regularize the corresponding likelihood-ratio test statistic. An efficient dynamic programming algorithm is developed to determine the optimal slicing scheme. Asymptotic and finite-sample properties such as power and null distribution of the resulting test statistic are studied. We compare the proposed testing method with some existing well-known methods and demonstrate its statistical power through extensive simulation studies as well as a real data example. A dynamic slicing method for the one-sample testing problem is further developed and studied under the same framework. Supplementary materials including technical derivations and proofs are available online.

• Dynamic programming
• Kolmogorov–Smirnov test
• Kullback–Leibler divergence
• Mutual information
• Regularization
• Two-sample test

Additional information

Notes on contributors

Bo Jiang

Bo Jiang, Department of Statistics, 1 Oxford Street, Harvard University, Cambridge, MA 02138 (E-mail: [email protected] ).

Chao Ye

Chao Ye, Bioinformatics Division and Center for Synthetic & Systems Biology, TNLIST and Department of Automation, Tsinghua University, Beijing 100084, China (E-mail: [email protected] ).

Jun S. Liu

Jun S. Liu is Professor of Statistics, Department of Statistics, Harvard University, Cambridge, MA 02138 (E-mail: [email protected] ).