Asymptotic power of sphericity tests for high-dimensional data

DOI10.1214/13-AOS1100zbMath1293.62125arXiv1306.4867MaRDI QIDQ366967

Alexei Onatski, Marcelo J. Moreira, Marc Hallin

Publication date: 25 September 2013

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

Full work available at URL: https://arxiv.org/abs/1306.4867

zbMATH Keywords

steepest descentcontiguityasymptotic powerpower envelopecontour integral representationlarge dimensionalitysphericity testsspiked covariance

Mathematics Subject Classification ID

Theory of statistical experiments (62B15) Hypothesis testing in multivariate analysis (62H15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60)

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Cites Work

• Unnamed Item
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• Unnamed Item
• A new test for sphericity of the covariance matrix for high dimensional data
• Limits of spiked random matrices. I
• Asymptotic power of sphericity tests for high-dimensional data
• Optimal detection of sparse principal components in high dimension
• The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source. I
• A Fourier view on the \(R\)-transform and related asymptotics of spherical integrals
• Convergence rate of expected spectral distributions of large random matrices. II: Sample covariance matrices
• Finite sample approximation results for principal component analysis: A matrix perturbation approach
• Corrections to LRT on large-dimensional covariance matrix by RMT
• On singular Wishart and singular multivariate beta distributions
• On the distribution of the largest eigenvalue in principal components analysis
• Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size
• Laplace approximations for hypergeometric functions with matrix argument
• Means of a Dirichlet process and multiple hypergeometric functions.
• CLT for linear spectral statistics of large-dimensional sample covariance matrices.
• On the empirical distribution of eigenvalues of a class of large dimensional random matrices
• Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices
• Semiparametrically efficient rank-based inference for shape. I: optimal rank-based tests for sphericity
• A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix
• Eigenvalues of large sample covariance matrices of spiked population models
• A note on testing the covariance matrix for large dimension
• Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
• THE DENSITY OF A QUADRATIC FORM IN A VECTOR UNIFORMLY DISTRIBUTED ON THE n-SPHERE
• The largest eigenvalues of sample covariance matrices for a spiked population: Diagonal case
• Rank 1 real Wishart spiked model
• Multiple Hypergeometric Functions: Probabilistic Interpretations and Statistical Uses
• Testing Hypotheses About the Number of Factors in Large Factor Models
• Asymptotic Statistics
• Sample Eigenvalue Based Detection of High-Dimensional Signals in White Noise Using Relatively Few Samples
• Non-Parametric Detection of the Number of Signals: Hypothesis Testing and Random Matrix Theory
• Tests for High-Dimensional Covariance Matrices
• Performance of Statistical Tests for Single-Source Detection Using Random Matrix Theory
• The distribution of a statistic used for testing sphericity of normal distributions
• Locally Best Invariant Test for Sphericity and the Limiting Distributions
• Distributions of Matrix Variates and Latent Roots Derived from Normal Samples
• Significance Test for Sphericity of a Normal $n$-Variate Distribution

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