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PreprintarXiv licencearXiv

A New Test for High-Dimensional Elliptical Distributions

  • Wenrui Wu
  • Bingye Yang
  • Minghua Deng
  • Xu Guo
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Abstract

Elliptical distributions provide a flexible and widely used extension of multivariate normal distribution. They play a critical role in many statistical procedures when dealing with high-dimensional data. However, goodness-of-fit testing for elliptical distributions remains challenging when the dimension p is comparable to or larger than the sample size n. In this work, we propose a new test for high-dimensional elliptical distributions. We establish high-dimensional Gaussian approximation for the test statistic under general correlation structures, allowing the dimension to grow as log p=o(n1/14) under finite moment conditions. We further develop Gaussian multiplier bootstrap test procedure and prove its theoretical validity. Numerical studies demonstrate stable finite-sample behavior and favorable power against a range of alternatives. Applications to real datasets illustrate practical utility of the proposed test.

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Cite

BibTeXRIS
BibTeX
@misc{wu2026test,
  title = {{A New Test for High-Dimensional Elliptical Distributions}},
  author = {Wenrui Wu and Bingye Yang and Minghua Deng and Xu Guo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.11304},
  eprint = {2607.11304},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.11304},
}
RIS
TY  - UNPB
TI  - A New Test for High-Dimensional Elliptical Distributions
AU  - Wenrui Wu
AU  - Bingye Yang
AU  - Minghua Deng
AU  - Xu Guo
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2607.11304
UR  - https://arxiv.org/abs/2607.11304
AB  - Elliptical distributions provide a flexible and widely used extension of multivariate normal distribution. They play a critical role in many statistical procedures when dealing with high-dimensional data. However, goodness-of-fit testing for elliptical distributions remains challenging when the dimension p is comparable to or larger than the sample size n. In this work, we propose a new test for high-dimensional elliptical distributions. We establish high-dimensional Gaussian approximation for the test statistic under general correlation structures, allowing the dimension to grow as log p=o(n^1/14) under finite moment conditions. We further develop Gaussian multiplier bootstrap test procedure and prove its theoretical validity. Numerical studies demonstrate stable finite-sample behavior and favorable power against a range of alternatives. Applications to real datasets illustrate practical utility of the proposed test.
ER  -