A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices

Hu, Jiang; Bai, Zhidong

doi:10.1007/s11425-016-0131-0

Cited by 34 publications

(16 citation statements)

References 49 publications

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“…Traditional approaches, which focus on low-dimensional and Euclidean data, often fail or are not easily generalizable to highdimensional and non-Euclidean data. Additionally, some recent developments in high-dimensional two-sample testing are limited to simple alternatives such as location and scale differences (see, Hu and Bai, 2016, for a recent review). In this context, there is a need to develop a new tool for the two-sample problem that can efficiently handle complex data and can detect differences beyond location and scale alternatives.…”

Section: Introductionmentioning

confidence: 99%

Global and local two-sample tests via regression

Kim¹,

Lee²,

Lei³

2019

Electron. J. Statist.

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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. arXiv:1812.08927v3 [stat.ME] 18 Nov 2019

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Section: Introductionmentioning

confidence: 99%

Global and local two-sample tests via regression

Kim¹,

Lee²,

Lei³

2019

Electron. J. Statist.

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“…, can be used. It has been established that Hotelling's 2 test is uniformly the most powerful test in a class of affine invariant test [1]. Capilla [2] considered the use of Hotelling's 2 test statistic in constructing a statistical control chart for wastewater treatment process.…”

Section: Letmentioning

confidence: 99%

On some Diagonalized and Regularized Hotelling’s T^2 Tests of Location for High Dimensional Data

Makinde¹,

Omotoso²

2020

Gazi University Journal of Science

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Highlights• A revisit to the diagonalized and regularized Hotelling's 2 tests. • Notions of data depth for trimming of mean vectors and covariance matrices. • Comparison of diagonalized and regularized Hotelling's 2 tests with the usual Hotelling's 2 test.• Limitations of diagonalized and regularized Hotelling's 2 tests in high dimension.• Proposal of robust versions of diagonalized and regularized Hotelling's 2 tests in high dimension.

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“…The problem becomes challenging when data have higher dimensions relative to their sizes and are in complex form (texts, curves, images, graphs etc.). Classical methods with a focus on testing the difference in the first or second moments of the distributions have become inadequate for such data and remedies have been suggested [1,3,4,5,9]. Other and more general methods have also been proposed.…”

Section: Introductionmentioning

confidence: 99%

Two‐sample test based on classification probability

Cai

Goggin

Jiang

2019

Statistical Analysis

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Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of classification probabilities from a classifier trained from the samples, a test statistic is proposed. We explain why such a test can be a powerful test and compare its performance in terms of the power and efficiency with those of some other recently proposed tests with simulation and real-life data. The test proposed is nonparametric and can be applied to complex and high dimensional data wherever there is a classifier that provides consistent estimate of the classification probability for such data.

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A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices

Cited by 34 publications

References 49 publications

Global and local two-sample tests via regression

Global and local two-sample tests via regression

On some Diagonalized and Regularized Hotelling’s T^2 Tests of Location for High Dimensional Data

Two‐sample test based on classification probability

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