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AN ADAPTIVE WEIGHTED COMPONENT TEST FOR HIGH-DIMENSIONAL MEANS

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Title: AN ADAPTIVE WEIGHTED COMPONENT TEST FOR HIGH-DIMENSIONAL MEANS
Authors: Qu, Yidi, Shu, Lianjie, Xu, Jinfeng
Source: Qu, Y, Shu, L & Xu, J 2024, 'AN ADAPTIVE WEIGHTED COMPONENT TEST FOR HIGH-DIMENSIONAL MEANS', Statistica Sinica, vol. 34, no. 4, pp. 1951-1971. https://doi.org/10.5705/ss.202022.0143
Publication Year: 2024
Subject Terms: High-dimensional test, Huber’s weight function, Testing equality of mean vectors, Weighted components, COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: Statistica Sinica © 2023 Institute of Statistical Science, Academia Sinica. Use of this article is permitted solely for educational and research purposes. Qu, Y., Shu, L., & Xu, J. (2024). AN ADAPTIVE WEIGHTED COMPONENT TEST FOR HIGH-DIMENSIONAL MEANS. Statistica Sinica, 34(4), 1951-1971. https://doi.org/10.5705/ss.202022.0143
Description: Two recent streams of two-sample tests for high-dimensional data are the sum-of-squares-based and supremum-based tests. The former is powerful against dense differences in two population means, and the latter is powerful against sparse differences. However, the level of sparsity and signal strength are often unknown, in practice, making it unclear which type of test to use. Here, we propose an adaptive weighted component test that provides good power against a variety of alternative hypotheses with unknown sparsity levels and varying signal strengths. The basic idea is to first allocate different weights to components with varying magnitudes in a sum-of-squares-based test, and then to combine multiple weighted component tests to make the underlying test adaptive to different sparsity levels of the mean differences. We examine the asymptotic properties of the proposed test, and use numerical comparisons to demonstrate the superior performance of the proposed test across a spectrum of situations.
Document Type: article in journal/newspaper
File Description: application/pdf
Language: English
ISSN: 1017-0405
1996-8507
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DOI: 10.5705/ss.202022.0143
Availability: https://scholars.cityu.edu.hk/en/publications/a4791c12-7e20-41c8-9abb-eca2a400f361
https://scholars.cityu.edu.hk/ws/files/166691276/158689588.pdf
https://doi.org/10.5705/ss.202022.0143
https://hdl.handle.net/2031/a4791c12-7e20-41c8-9abb-eca2a400f361
Rights: info:eu-repo/semantics/openAccess
Accession Number: edsbas.8A068F02
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  Data: AN ADAPTIVE WEIGHTED COMPONENT TEST FOR HIGH-DIMENSIONAL MEANS
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  Data: Qu, Y, Shu, L & Xu, J 2024, 'AN ADAPTIVE WEIGHTED COMPONENT TEST FOR HIGH-DIMENSIONAL MEANS', Statistica Sinica, vol. 34, no. 4, pp. 1951-1971. https://doi.org/10.5705/ss.202022.0143
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  Data: <searchLink fieldCode="DE" term="%22High-dimensional+test%22">High-dimensional test</searchLink><br /><searchLink fieldCode="DE" term="%22Huber%27s+weight+function%22">Huber’s weight function</searchLink><br /><searchLink fieldCode="DE" term="%22Testing+equality+of+mean+vectors%22">Testing equality of mean vectors</searchLink><br /><searchLink fieldCode="DE" term="%22Weighted+components%22">Weighted components</searchLink><br /><searchLink fieldCode="DE" term="%22COPYRIGHT+TERMS+OF+DEPOSITED+FINAL+PUBLISHED+VERSION+FILE%3A+Statistica+Sinica+©+2023+Institute+of+Statistical+Science%22">COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: Statistica Sinica © 2023 Institute of Statistical Science</searchLink><br /><searchLink fieldCode="DE" term="%22Academia+Sinica%2E+Use+of+this+article+is+permitted+solely+for+educational+and+research+purposes%2E+Qu%22">Academia Sinica. Use of this article is permitted solely for educational and research purposes. Qu</searchLink><br /><searchLink fieldCode="DE" term="%22Y%2E%22">Y.</searchLink><br /><searchLink fieldCode="DE" term="%22Shu%22">Shu</searchLink><br /><searchLink fieldCode="DE" term="%22L%2E%22">L.</searchLink><br /><searchLink fieldCode="DE" term="%22%26+Xu%22">& Xu</searchLink><br /><searchLink fieldCode="DE" term="%22J%2E+%282024%29%2E+AN+ADAPTIVE+WEIGHTED+COMPONENT+TEST+FOR+HIGH-DIMENSIONAL+MEANS%2E+Statistica+Sinica%22">J. (2024). AN ADAPTIVE WEIGHTED COMPONENT TEST FOR HIGH-DIMENSIONAL MEANS. Statistica Sinica</searchLink><br /><searchLink fieldCode="DE" term="%2234%284%29%22">34(4)</searchLink><br /><searchLink fieldCode="DE" term="%221951-1971%2E+https%3A%2F%2Fdoi%2Eorg%2F10%2E5705%2Fss%2E202022%2E0143%22">1951-1971. https://doi.org/10.5705/ss.202022.0143</searchLink>
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  Data: Two recent streams of two-sample tests for high-dimensional data are the sum-of-squares-based and supremum-based tests. The former is powerful against dense differences in two population means, and the latter is powerful against sparse differences. However, the level of sparsity and signal strength are often unknown, in practice, making it unclear which type of test to use. Here, we propose an adaptive weighted component test that provides good power against a variety of alternative hypotheses with unknown sparsity levels and varying signal strengths. The basic idea is to first allocate different weights to components with varying magnitudes in a sum-of-squares-based test, and then to combine multiple weighted component tests to make the underlying test adaptive to different sparsity levels of the mean differences. We examine the asymptotic properties of the proposed test, and use numerical comparisons to demonstrate the superior performance of the proposed test across a spectrum of situations.
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        Value: 10.5705/ss.202022.0143
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        Type: general
      – SubjectFull: Huber’s weight function
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      – SubjectFull: Testing equality of mean vectors
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      – SubjectFull: Weighted components
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      – SubjectFull: J. (2024). AN ADAPTIVE WEIGHTED COMPONENT TEST FOR HIGH-DIMENSIONAL MEANS. Statistica Sinica
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