高维度 Hotelling $$T^2$ 检验与 Wilks 离群值方法的应用

IF 1.2 3区数学 Q2 STATISTICS & PROBABILITY

Statistical Papers Pub Date : 2024-07-19 DOI:10.1007/s00362-024-01587-5

Reza Modarres

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引用次数: 0

摘要

我们考虑了低样本量、高维度环境下的$T^2$ 检验。我们将 p 个变量划分为 p/b 个变量的 $b>1$ 块，并利用联合-交集原理提出了一种在每个块中计算 $T^2$ 检验的检验过程。我们证明了所提出的方法比 Hotelling $T^2$ 检验更强大。我们还考虑了离群值检测的 Wilks 方法，并使用联合-交集原理在变量块中搜索离群值。我们研究了新检验的显著性水平和幂函数。结果表明，与 Wilks 检验相比，新的离群值检测方法能产生更大的检验功率。

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Hotelling $$T^2$$ test in high dimensions with application to Wilks outlier method

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Hotelling $$T^2$$ test in high dimensions with application to Wilks outlier method

We consider the Hotelling $T^2$ test in low sample size, high dimensional setting. We partition the p variables into $b>1$ blocks of p/b variables and use the union-intersection principle to propose a testing procedure that computes the $T^2$ test in each block. We show that the proposed method is more powerful than Hotelling $T^2$ test. We also consider Wilks method of outlier detection and use the union-intersection principle to search for outliers in blocks of variables. The significance level and the power function of the new test are investigated. We show that the new outlier detection method produces more power compared to Wilks test.

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来源期刊

Statistical Papers 数学-统计学与概率论

CiteScore

2.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal Statistical Papers addresses itself to all persons and organizations that have to deal with statistical methods in their own field of work. It attempts to provide a forum for the presentation and critical assessment of statistical methods, in particular for the discussion of their methodological foundations as well as their potential applications. Methods that have broad applications will be preferred. However, special attention is given to those statistical methods which are relevant to the economic and social sciences. In addition to original research papers, readers will find survey articles, short notes, reports on statistical software, problem section, and book reviews.