Consistency of AIC and BIC in estimating the number of significant components in high-dimensional principal component analysis

DOI10.1214/17-AOS1577zbMath1395.62119OpenAlexW2799861551MaRDI QIDQ1650069

Kwok Pui Choi, Yasunori Fujikoshi, Zhi-Dong Bai

Publication date: 29 June 2018

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

Full work available at URL: https://projecteuclid.org/euclid.aos/1525313075

zbMATH Keywords

consistencyprincipal component analysisdimensionalityAICBIChigh-dimensional asymptotic framework

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Asymptotic distribution theory in statistics (62E20)

Related Items

Generalized \(k\)-means in GLMs with applications to the outbreak of COVID-19 in the United States, Wigner and Wishart ensembles for sparse Vinberg models, Non-asymptotic properties of spectral decomposition of large Gram-type matrices and applications, Variance variation criterion and consistency in estimating the number of significant signals of high-dimensional PCA, A generalized information criterion for high-dimensional PCA rank selection, Asymptotics of AIC, BIC and \(C_p\) model selection rules in high-dimensional regression, Asymptotic Optimality of Cp-Type Criteria in High-Dimensional Multivariate Linear Regression Models, Hybrid Kronecker Product Decomposition and Approximation, Limiting laws for divergent spiked eigenvalues and largest nonspiked eigenvalue of sample covariance matrices, Order determination for spiked-type models with a divergent number of spikes, Generalized four moment theorem and an application to CLT for spiked eigenvalues of high-dimensional covariance matrices, Canonical correlation coefficients of high-dimensional Gaussian vectors: finite rank case, Consistent selection of the number of change-points via sample-splitting, The generalized degrees of freedom of multilinear principal component analysis, Determining the number of canonical correlation pairs for high-dimensional vectors, Random matrix theory and its applications, Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• High-dimensional consistency of rank estimation criteria in multivariate linear model
• Consistency of high-dimensional AIC-type and \(C_p\)-type criteria in multivariate linear regression
• Selection of components in principal component analysis: A comparison of methods
• Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
• On sample eigenvalues in a generalized spiked population model
• Asymptotic properties of criteria for selection of variables in multiple regression
• Strong consistency of the information criterion for model selection in multivariate analysis
• Estimating the dimension of a model
• No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices
• On estimating the dimensionality in canonical correlation analysis
• On detection of the number of signals in presence of white noise
• On the distribution of the largest eigenvalue in principal components analysis
• Principal component analysis.
• Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices
• A consistency property of the AIC for multivariate linear models when the dimension and the sample size are large
• Asymptotic distribution of the LR statistic for equality of the smallest eigenvalues in high-dimensional principal component analysis
• A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix
• Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation
• Selection of the order of an autoregressive model by Akaike's information criterion
• On Consistency and Sparsity for Principal Components Analysis in High Dimensions
• Multivariate Statistics