An adaptable generalization of Hotelling's $T^2$ test in high dimension

DOI10.48550/arXiv.1609.08725zbMath1451.62083arXiv1609.08725OpenAlexW3042820579MaRDI QIDQ151159

Jie Peng, Alexander Aue, Pei Wang, Debashis Paul, Haoran Li, Jie Peng, Pei Wang, Debashis Paul, Alexander Aue, Hao-Ran Li

Publication date: 28 September 2016

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.08725

zbMATH Keywords

hypothesis testingcovariance matrixrandom matrix theoryasymptotic propertyHotelling's \(T^2\) statisticlocally most powerful tests

Mathematics Subject Classification ID

Gaussian processes (60G15) Applications of statistics to biology and medical sciences; meta analysis (62P10) Hypothesis testing in multivariate analysis (62H15) Measures of association (correlation, canonical correlation, etc.) (62H20) Random matrices (probabilistic aspects) (60B20) Random matrices (algebraic aspects) (15B52) Analysis of variance and covariance (ANOVA) (62J10)

Related Items

A rank-based high-dimensional test for equality of mean vectors, An RIHT statistic for testing the equality of several high-dimensional mean vectors under homoskedasticity, Finite sample \(t\)-tests for high-dimensional means, Nonparametric Two-Sample Tests of High Dimensional Mean Vectors via Random Integration, Limiting distributions of graph-based test statistics on sparse and dense graphs, A Pairwise Hotelling Method for Testing High-Dimensional Mean Vectors, High-dimensional general linear hypothesis tests via non-linear spectral shrinkage, ARHT, High-dimensional linear models: a random matrix perspective, An overview of tests on high-dimensional means, Recent developments in high-dimensional inference for multivariate data: parametric, semiparametric and nonparametric approaches

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A nonparametric two-sample test applicable to high dimensional data
• Eigenvectors of some large sample covariance matrix ensembles
• Central limit theorem for Hotelling's \(T^{2}\) statistic under large dimension
• Shrinkage-based diagonal Hotelling's tests for high-dimensional small sample size data
• Fluctuations of eigenvalues and second order Poincaré inequalities
• A test for the mean vector with fewer observations than the dimension under non-normality
• Spectral analysis of large dimensional random matrices
• No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices
• Tests for high-dimensional data based on means, spatial signs and spatial ranks
• On the Marčenko-Pastur law for linear time series
• A two-sample test for high-dimensional data with applications to gene-set testing
• Random matrix theory in statistics: a review
• A test for the mean vector with fewer observations than the dimension
• A Regularized Hotelling’sT²Test for Pathway Analysis in Proteomic Studies
• Two-Sample Test of High Dimensional Means Under Dependence
• ON ESTIMATION OF THE POPULATION SPECTRAL DISTRIBUTION FROM A HIGH‐DIMENSIONAL SAMPLE COVARIANCE MATRIX
• A Two-Sample Test for Equality of Means in High Dimension
• A High-Dimensional Nonparametric Multivariate Test for Mean Vector
• Tests for High Dimensional Generalized Linear Models
• An adaptive two-sample test for high-dimensional means