Consistency of an Information Criterion for High-Dimensional Multivariate Regression, 1st ed. 2024
JSS Research Series in Statistics Series

This is the first book on an evaluation of (weak) consistency of an information criterion for variable selection in high-dimensional multivariate linear regression models by using the high-dimensional asymptotic framework. It is an asymptotic framework such that the sample size n and the dimension of response variables vector p are approaching ? simultaneously under a condition that p/n goes to a constant included in [0,1).Most statistical textbooks evaluate consistency of an information criterion by using the large-sample asymptotic framework such that n goes to ? under the fixed p. The evaluation of consistency of an information criterion from the high-dimensional asymptotic framework provides new knowledge to us, e.g., Akaike's information criterion (AIC) sometimes becomes consistent under the high-dimensional asymptotic framework although it never has a consistency under the large-sample asymptotic framework; and Bayesian information criterion (BIC) sometimes becomes inconsistent under the high-dimensional asymptotic framework although it is always consistent under the large-sample asymptotic framework. The knowledge may help to choose an information criterion to be used for high-dimensional data analysis, which has been attracting the attention of many researchers.

Reevaluates the consistency of an information criterion by the high-dimensional asymptotic framework

Deals with the high-dimensional asymptotic theory when the normality assumption is violated

Considers a wide class of information criteria