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arXiv · 2607.11304

A Correlation-Free 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 is comparable to or larger than the sample size. In this work, we propose a correlation-free 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, without using the inverse sample covariance matrix. 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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Wenrui Wu, Bingye Yang, Minghua Deng, Xu Guo. 2026-07-13. A Correlation-Free Test for High-Dimensional Elliptical Distributions. https://arxiv.org/abs/2607.11304

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