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A remark on moment-dependent phase transitions in high-dimensional Gaussian approximations

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  • Kock, Anders Bredahl
  • Preinerstorfer, David

Abstract

In this article, we study the critical growth rates of dimension below which Gaussian critical values can be used for hypothesis testing but beyond which they cannot. We are particularly interested in how these growth rates depend on the number of moments that the observations possess.

Suggested Citation

  • Kock, Anders Bredahl & Preinerstorfer, David, 2024. "A remark on moment-dependent phase transitions in high-dimensional Gaussian approximations," Statistics & Probability Letters, Elsevier, vol. 211(C).
    • Handle: RePEc:eee:stapro:v:211:y:2024:i:c:s0167715224001184
    DOI: 10.1016/j.spl.2024.110149
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    References listed on IDEAS

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    1. Victor Chernozhukov & Denis Chetverikov & Kengo Kato & Yuta Koike, 2019. "Improved Central Limit Theorem and bootstrap approximations in high dimensions," Papers 1912.10529, arXiv.org, revised May 2022.
    2. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
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