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May 2019 An extreme-value approach for testing the equality of large U-statistic based correlation matrices
Cheng Zhou, Fang Han, Xin-Sheng Zhang, Han Liu
Bernoulli 25(2): 1472-1503 (May 2019). DOI: 10.3150/18-BEJ1027

Abstract

There has been an increasing interest in testing the equality of large Pearson’s correlation matrices. However, in many applications it is more important to test the equality of large rank-based correlation matrices since they are more robust to outliers and nonlinearity. Unlike the Pearson’s case, testing the equality of large rank-based statistics has not been well explored and requires us to develop new methods and theory. In this paper, we provide a framework for testing the equality of two large U-statistic based correlation matrices, which include the rank-based correlation matrices as special cases. Our approach exploits extreme value statistics and the Jackknife estimator for uncertainty assessment and is valid under a fully nonparametric model. Theoretically, we develop a theory for testing the equality of U-statistic based correlation matrices. We then apply this theory to study the problem of testing large Kendall’s tau correlation matrices and demonstrate its optimality. For proving this optimality, a novel construction of least favorable distributions is developed for the correlation matrix comparison.

Citation

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Cheng Zhou. Fang Han. Xin-Sheng Zhang. Han Liu. "An extreme-value approach for testing the equality of large U-statistic based correlation matrices." Bernoulli 25 (2) 1472 - 1503, May 2019. https://doi.org/10.3150/18-BEJ1027

Information

Received: 1 January 2017; Revised: 1 February 2018; Published: May 2019
First available in Project Euclid: 6 March 2019

zbMATH: 07049413
MathSciNet: MR3920379
Digital Object Identifier: 10.3150/18-BEJ1027

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 2 • May 2019
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