Exponential bounds for regularized Hotelling’s T2 statistic in high dimension

IF 1.4 3区 数学 Q2 STATISTICS & PROBABILITY
El Mehdi Issouani , Patrice Bertail , Emmanuelle Gautherat
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引用次数: 0

Abstract

We obtain exponential inequalities for regularized Hotelling’s Tn2 statistics, that take into account the potential high dimensional aspects of the problem. We explore the finite sample properties of the tail of these statistics by deriving exponential bounds for symmetric distributions and also for general distributions under weak moment assumptions (we never assume exponential moments). For this, we use a penalized estimator of the covariance matrix and propose an optimal choice for the penalty coefficient.

正则化霍特林 Tn2 的指数边界
我们获得了正则化霍特林 Tn2 统计量的指数不等式,其中考虑到了问题的潜在高维方面。我们通过推导对称分布以及弱矩假设下一般分布(我们从不假设指数矩)的指数边界,探索了这些统计量尾部的有限样本特性。为此,我们使用了协方差矩阵的惩罚估计器,并提出了惩罚系数的最优选择。
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来源期刊
Journal of Multivariate Analysis
Journal of Multivariate Analysis 数学-统计学与概率论
CiteScore
2.40
自引率
25.00%
发文量
108
审稿时长
74 days
期刊介绍: Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data. The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of Copula modeling Functional data analysis Graphical modeling High-dimensional data analysis Image analysis Multivariate extreme-value theory Sparse modeling Spatial statistics.
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