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Linear Hypothesis Testing in Linear Models With High-Dimensional Responses

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  • Changcheng Li Runze Li

Abstract

In this article, we propose a new projection test for linear hypotheses on regression coefficient matrices in linear models with high-dimensional responses. We systematically study the theoretical properties of the proposed test. We first derive the optimal projection matrix for any given projection dimension to achieve the best power and provide an upper bound for the optimal dimension of projection matrix. We further provide insights into how to construct the optimal projection matrix. One- and two-sample mean problems can be formulated as special cases of linear hypotheses studied in this article. We both theoretically and empirically demonstrate that the proposed test can outperform the existing ones for one- and two-sample mean problems. We conduct Monte Carlo simulation to examine the finite sample performance and illustrate the proposed test by a real data example.

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  • Changcheng Li Runze Li, 2022. "Linear Hypothesis Testing in Linear Models With High-Dimensional Responses," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(540), pages 1738-1750, October.
    • Handle: RePEc:taf:jnlasa:v:117:y:2022:i:540:p:1738-1750
    DOI: 10.1080/01621459.2021.1884561
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    Cited by:

    1. Li, Jun, 2023. "Finite sample t-tests for high-dimensional means," Journal of Multivariate Analysis, Elsevier, vol. 196(C).

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