Central limit theorem for Hotelling's \(T^{2}\) statistic under large dimension

DOI10.1214/10-AAP742zbMath1250.62030arXiv0802.0082OpenAlexW3100254145MaRDI QIDQ655585

Wang Zhou, Guangming Pan

Publication date: 4 January 2012

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

Full work available at URL: https://arxiv.org/abs/0802.0082

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Hypothesis testing in multivariate analysis (62H15) Central limit and other weak theorems (60F05) Strong limit theorems (60F15)

Related Items (17)

Self-normalization: taming a wild population in a heavy-tailed world ⋮ Proposition of new alternative tests adapted to the traditional T² test ⋮ A p-value based dimensionality reduction test for high dimensional means ⋮ High-dimensional general linear hypothesis tests via non-linear spectral shrinkage ⋮ Unnamed Item ⋮ Comparison between two types of large sample covariance matrices ⋮ On LR simultaneous test of high-dimensional mean vector and covariance matrix under non-normality ⋮ Random matrix theory in statistics: a review ⋮ Test for high-dimensional mean vector under missing observations ⋮ Limiting behavior of eigenvalues in high-dimensional MANOVA via RMT ⋮ A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices ⋮ On the dimension effect of regularized linear discriminant analysis ⋮ Sign-based test for mean vector in high-dimensional and sparse settings ⋮ An adaptable generalization of Hotelling's $T^2$ test in high dimension ⋮ High-dimensional linear models: a random matrix perspective ⋮ CLT for spiked eigenvalues of a sample covariance matrix from high-dimensional Gaussian mean mixtures ⋮ CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size

Cites Work

• Weak convergence of random functions defined by the eigenvectors of sample covariance matrices
• Central limit theorem for signal-to-interference ratio of reduced rank linear receiver
• Almost sure limit of the smallest eigenvalue of some sample correlation matrices
• On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
• On the eigenvectors of large dimensional sample covariance matrices
• Some limit theorems for the eigenvalues of a sample covariance matrix
• Distribution function inequalities for martingales
• The strong limits of random matrix spectra for sample matrices of independent elements
• No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices
• Limiting spectral distribution for a class of random matrices
• On the distribution of the largest eigenvalue in principal components analysis
• CLT for linear spectral statistics of large-dimensional sample covariance matrices.
• Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices
• On fluctuations of eigenvalues of random Hermitian matrices.
• On asymptotics of eigenvectors of large sample covariance matrix
• Linear functionals of eigenvalues of random matrices
• Central limit theorem for traces of large random symmetric matrices with independent matrix elements
• The Generalization of Student's Ratio
• Testing Statistical Hypotheses
• DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Central limit theorem for Hotelling's \(T^{2}\) statistic under large dimension