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

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  • Anders Bredahl Kock
  • David Preinerstorfer

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

  • Anders Bredahl Kock & David Preinerstorfer, 2023. "A remark on moment-dependent phase transitions in high-dimensional Gaussian approximations," Papers 2310.12863, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2310.12863
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    References listed on IDEAS

    as
    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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