用u统计量检验高维协方差矩阵的恒等性和球性

IF 1.6 3区数学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computational Statistics & Data Analysis Pub Date : 2025-07-05 DOI:10.1016/j.csda.2025.108242

Xiaoge Xiong

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引用次数: 0

摘要

提出了两种新的检验方法来检验高维渐近框架中协方差矩阵的恒等性和球性，这两种检验方法都是用u统计量构造的。这些检验的极限分布是在零假设和局部备用假设下建立的。蒙特卡罗仿真结果表明，在各种情况下，该方法优于几种竞争方法，所提出的测试在密集和稀疏替代方案下都能达到全功率。通过对冒号数据集的应用程序进一步验证了所建议测试的有效性。

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New tests for the identity and sphericity of high-dimensional covariance matrices via U-statistics

Two novel test procedures are proposed for the identity and sphericity of covariance matrices in high-dimensional asymptotic frameworks, both constructed via U-statistics. The limiting distributions of these tests are established under null and local alternative hypotheses. Monte Carlo simulation results demonstrate their superiority over several competing methods across various scenarios, with the proposed tests achieving full power against both dense and sparse alternatives. The effectiveness of the proposed tests is further validated through an application to a colon dataset.

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来源期刊

Computational Statistics & Data Analysis 数学-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

167

审稿时长

60 days

期刊介绍： Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas: I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article. II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures. [...] III) Special Applications - [...] IV) Annals of Statistical Data Science [...]