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Statistics > Methodology

arXiv:2204.08628 (stat)
[Submitted on 19 Apr 2022 (v1), last revised 2 Aug 2023 (this version, v2)]

Title:Asymptotic Independence of the Quadratic form and Maximum of Independent Random Variables with Applications to High-Dimensional Tests

Authors:Dachuan Chen, Decai Liang, Long Feng
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Abstract:This paper establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and maximum, which can be applied into the high-dimensional testing problems. By combining the sum-type test and the max-type test, we propose the Fisher's combination tests for the one-sample mean test and two-sample mean test. Under this novel general framework, several strong assumptions in existing literature have been relaxed. Monte Carlo simulation has been done which shows that our proposed tests are strongly robust to both sparse and dense data.
Subjects: Methodology (stat.ME)
Cite as: arXiv:2204.08628 [stat.ME]
  (or arXiv:2204.08628v2 [stat.ME] for this version)
  https://doi.org/10.48550/arXiv.2204.08628

Submission history

From: Long Feng [view email]
[v1] Tue, 19 Apr 2022 03:01:26 UTC (388 KB)
[v2] Wed, 2 Aug 2023 14:46:48 UTC (421 KB)
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