Open Access
2019 Global and local two-sample tests via regression
Ilmun Kim, Ann B. Lee, Jing Lei
Electron. J. Statist. 13(2): 5253-5305 (2019). DOI: 10.1214/19-EJS1648


Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature, there have been recent methodological developments such as classification accuracy tests. The goal of this work is to present a regression approach to comparing multivariate distributions of complex data. Depending on the chosen regression model, our framework can efficiently handle different types of variables and various structures in the data, with competitive power under many practical scenarios. Whereas previous work has been largely limited to global tests which conceal much of the local information, our approach naturally leads to a local two-sample testing framework in which we identify local differences between multivariate distributions with statistical confidence. We demonstrate the efficacy of our approach both theoretically and empirically, under some well-known parametric and nonparametric regression methods. Our proposed methods are applied to simulated data as well as a challenging astronomy data set to assess their practical usefulness.


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Ilmun Kim. Ann B. Lee. Jing Lei. "Global and local two-sample tests via regression." Electron. J. Statist. 13 (2) 5253 - 5305, 2019.


Received: 1 May 2019; Published: 2019
First available in Project Euclid: 17 December 2019

zbMATH: 07147376
MathSciNet: MR4043073
Digital Object Identifier: 10.1214/19-EJS1648

Primary: 62G10 , 62H15
Secondary: 62G20

Keywords: Galaxy morphology , intrinsic dimension , kernel regression , Nearest neighbor regression , Permutation test , random forests

Vol.13 • No. 2 • 2019
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