基于线性结构协方差矩阵的高维数据均值检验

IF 0.9 4区 数学 Q3 STATISTICS & PROBABILITY
Metrika Pub Date : 2024-07-02 DOI:10.1007/s00184-024-00971-3
Guanpeng Wang, Yuyuan Wang, Hengjian Cui
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引用次数: 0

摘要

在本研究中,当协方差矩阵尽可能表示为线性结构时,均值检验是在维数 p 远大于样本量 n 的条件下考虑的。首先,构建协方差矩阵线性结构中系数的估计器,然后自然给出有效的协方差矩阵估计器。接着,通过用给定的协方差矩阵估计器代替样本协方差矩阵,提出了一种类似于经典霍特林(T^2\)检验的新检验统计量。然后,在一些温和的条件下,分别得到了系数估计值的渐近正态性和均值检验的新统计量的渐近正态性。仿真结果表明,所提出的检验统计量与已知协方差矩阵的 Hotelling's \(T^2\) 检验统计量的性能几乎相同。我们的新检验统计量不仅能合理地控制名义水平,还能获得比其他竞争检验更大的经验力量。研究发现,在考虑协方差矩阵的结构信息时,均值检验的功率有很大提高,尤其是在高维情况下。此外,我们还提供了一个真实数据的例子来说明我们的方法的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Mean test for high-dimensional data based on covariance matrix with linear structures

Mean test for high-dimensional data based on covariance matrix with linear structures

In this work, the mean test is considered under the condition that the number of dimensions p is much larger than the sample size n when the covariance matrix is represented as a linear structure as possible. At first, the estimator of coefficients in the linear structures of the covariance matrix is constructed, and then an efficient covariance matrix estimator is naturally given. Next, a new test statistic similar to the classical Hotelling’s \(T^2\) test is proposed by replacing the sample covariance matrix with the given estimator of covariance matrix. Then the asymptotic normality of the estimator of coefficients and that of a new statistic for the mean test are separately obtained under some mild conditions. Simulation results show that the performance of the proposed test statistic is almost the same as the Hotelling’s \(T^2\) test statistic for which the covariance matrix is known. Our new test statistic can not only control reasonably the nominal level; it also gains greater empirical powers than competing tests. It is found that the power of mean test has great improvement when considering the structure information of the covariance matrix, especially for high-dimensional cases. Moreover, an example with real data is provided to show the application of our approach.

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来源期刊
Metrika
Metrika 数学-统计学与概率论
CiteScore
1.50
自引率
14.30%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Metrika is an international journal for theoretical and applied statistics. Metrika publishes original research papers in the field of mathematical statistics and statistical methods. Great importance is attached to new developments in theoretical statistics, statistical modeling and to actual innovative applicability of the proposed statistical methods and results. Topics of interest include, without being limited to, multivariate analysis, high dimensional statistics and nonparametric statistics; categorical data analysis and latent variable models; reliability, lifetime data analysis and statistics in engineering sciences.
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