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High-dimensional Tests for mean vector: Approaches without Estimating the mean vector Directly

Acta Mathematicae Applicatae Sinica 2022年第1期38卷 78-86页

作者： Bo CHEN Hai-meng WANG School of Mathematics and Information Technology Jiangsu Second Normal UniversityNanjing 211200China

Several tests for multivariate mean vector have been proposed in the recent ***,these tests are directly concerned with the mean vector of a high-dimensional *** paper presents two new test procedures for testing mean vector in large dimension and small *** do not focus on the mean vector directly,which is a different framework from the existing *** first test procedure is based on the asymptotic distribution of the test statistic,where the dimension increases with the sample *** second test procedure is based on the permutation distribution of the test statistic,where the sample size is fixed and the dimension grows to *** are carried out to examine the finite-sample performance of the tests and to compare them with some popular nonparametric tests available in the literature.

关键词： asymptotic distribution high-dimensional data permutation test U-statistic testing mean vector

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Sign-based Test for mean vector in High-dimensional and Sparse Settings

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Acta Mathematica Sinica,English Series 2020年第1期36卷 93-108页

作者： Wei LIU Ying Qiu LI College of Mathematics and Statistics Hu'nan University of Finance and EconomicsChangsha 410205P.R.China School of Mathematics and Statistics Changsha University of Science and TechnologyChangsha 410114P.R.China

In this article, we introduce a robust sparse test statistic which is based on the maximum type statistic. Both the limiting null distribution of the test statistic and the power of the test are analysed. It is shown that the test is particularly powerful against sparse alternatives. Numerical studies are carried out to examine the numerical performance of the test and to compare it with other tests available in the literature. The numerical results show that the test proposed significantly outperforms those tests in a range of settings, especially for sparse alternatives.

关键词： High-dimensional data maximum type test sign-based dense test sign-based sparsity test sum of squares type test testing mean vector

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