发表机构
School of Mathematical Sciences, Peking University; School of Statistics, Beijing Normal University（北京大学数学科学学院; 北京师范大学统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对高维椭圆分布拟合优度检验难题，提出无相关性检验，在一般相关结构下为检验统计量建立高维高斯近似，开发高斯乘数自助检验程序，经数值研究和实际应用验证其有限样本行为稳定、功效良好及实用价值。
AI 中文摘要
椭圆分布是多元正态分布灵活且广泛使用的扩展，在处理高维数据的许多统计过程中起关键作用。但当维度与样本量可比或更大时，椭圆分布的拟合优度检验仍具挑战性。本文提出高维椭圆分布的无相关性检验，在一般相关结构下为检验统计量建立高维高斯近似，在有限矩条件下允许维度按$\log p=o(n^{1/14})$增长，且无需使用逆样本协方差矩阵。还开发了高斯乘数自助检验程序并证明其理论有效性。数值研究表明其有限样本行为稳定，对多种备择假设具有良好功效，实际数据集应用展示了该检验的实用价值。
英文摘要
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.
Comments25 pages, 6 figures
