Consistency of high-dimensional AIC-type and \(C_p\)-type criteria in multivariate linear regression

DOI10.1016/j.jmva.2013.09.006zbMath1360.62265OpenAlexW2000436178MaRDI QIDQ391928

Hirokazu Yanagihara, Tetsuro Sakurai, Yasunori Fujikoshi

Publication date: 13 January 2014

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmva.2013.09.006

zbMATH Keywords

AICconsistency property\(C_p\)high-dimensional criteriamodified criteriamultivariate linear regression

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Classification and discrimination; cluster analysis (statistical aspects) (62H30)

Related Items (18)

High-dimensional consistency of rank estimation criteria in multivariate linear model ⋮ Consistency of AIC and BIC in estimating the number of significant components in high-dimensional principal component analysis ⋮ Variance variation criterion and consistency in estimating the number of significant signals of high-dimensional PCA ⋮ High-dimensional asymptotic behavior of the difference between the log-determinants of two Wishart matrices ⋮ A high-dimensional bias-corrected AIC for selecting response variables in multivariate calibration ⋮ A fast and consistent variable selection method for high-dimensional multivariate linear regression with a large number of explanatory variables ⋮ High-dimensional AIC in the growth curve model ⋮ 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 ⋮ Inadmissibility of the corrected Akaike information criterion ⋮ Unnamed Item ⋮ Model averaging for multivariate multiple regression models ⋮ Generalized ridge estimator and model selection criteria in multivariate linear regression ⋮ Covariance components selection in high-dimensional growth curve model with random coefficients ⋮ Consistent variable selection criteria in multivariate linear regression even when dimension exceeds sample size ⋮ High-dimensional consistencies of KOO methods in multivariate regression model and discriminant analysis ⋮ Consistency of test-based method for selection of variables in high-dimensional two-group discriminant analysis ⋮ Unnamed Item

Cites Work

• A criterion for variable selection in multiple discriminant analysis
• High-dimensional asymptotic expansions for the distributions of canonical correlations
• An unbiased \(C_p\) criterion for multivariate ridge regression
• The multivariate C_p
• Testing for complete independence in high dimensions
• Selection of the order of an autoregressive model by Akaike's information criterion
• Modified AIC and Cp in multivariate linear regression
• Model Selection for Multivariate Regression in Small Samples
• Some Comments on C P
• Multivariate Statistics
• Unnamed Item
• Unnamed Item

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