High Dimensional Analysis of Variance in Multivariate Linear Regression Article Swipe

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Zhipeng Lou , Xianyang Zhang , Wei Biao Wu ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2301.04209

In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type test statistic to test linear hypotheses and establish a high dimensional Gaussian approximation result under fairly mild moment assumptions. Our general framework and theory can be applied to deal with the classical one-way multivariate ANOVA and the nonparametric one-way MANOVA in high dimensions. To implement the test procedure in practice, we introduce a sample-splitting based estimator of the second moment of the error covariance and discuss its properties. A simulation study shows that our proposed test outperforms some existing tests in various settings.

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Multivariate Analysis Of Variance

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Multivariate analysis of variance Multivariate statistics Test statistic Mathematics Statistics Estimator Statistic Moment (physics) Nonparametric statistics Covariance Dimension (graph theory) Linear model Linear regression Gaussian Econometrics Statistical hypothesis testing Combinatorics Classical mechanics Quantum mechanics Physics

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2301.04209
PDF: https://arxiv.org/pdf/2301.04209
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4315881228

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DOI: https://doi.org/10.48550/arxiv.2301.04209

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Title: High Dimensional Analysis of Variance in Multivariate Linear Regression

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Type: preprint

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Language: en

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Publication year: 2023

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Publication date: 2023-01-10

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Authors: Zhipeng Lou, Xianyang Zhang, Wei Biao Wu

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Landing page: https://arxiv.org/abs/2301.04209

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PDF URL: https://arxiv.org/pdf/2301.04209

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Concepts: Multivariate analysis of variance, Multivariate statistics, Test statistic, Mathematics, Statistics, Estimator, Statistic, Moment (physics), Nonparametric statistics, Covariance, Dimension (graph theory), Linear model, Linear regression, Gaussian, Econometrics, Statistical hypothesis testing, Combinatorics, Classical mechanics, Quantum mechanics, Physics

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