High-dimensionality-adjusted consistent AIC in normal multivariate linear regression

For multivariate models, one of the important properties of a variable selection criterion is consistency, whereby the probability of selecting the true subset of explanatory variables approaches 1 as the sample size goes to infinity. However, in cases of high-dimensionality, the BIC, which is expec...

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Bibliographic Details
Published in:Procedia computer science 2024, Vol.246, p.2022-2031
Main Author: Yanagihara, Hirokazu
Format: Article
Language:English
Subjects:
consistency
generalized information criterion
high-dimensional
large-sample asymptotic framework
normal multivariate linear regression
variable selection
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Summary:For multivariate models, one of the important properties of a variable selection criterion is consistency, whereby the probability of selecting the true subset of explanatory variables approaches 1 as the sample size goes to infinity. However, in cases of high-dimensionality, the BIC, which is expected to be consistent under large-sample asymptotic theory, may not be consistent, and the AIC, which is said to be inconsistent under the same large-sample asymptotic theory, may be consistent. In this paper, we propose a high-dimensionality-adjusted consistent AIC called the HCAIC, which is an adjusted version of the consistent AIC proposed by Bozdogan (1987) regarding the effect of high-dimensionality through an asymptotic theory whereby the dimension of the vector of response variables allows both an increasing and a fixed condition as sample size increases. Through a series of numerical experiments, we verify that the proposed HCAIC is a high-performance information criterion in the sense that it can select the true subset of explanatory variables with high probability for any dimensionality.
ISSN:1877-0509
1877-0509
DOI:10.1016/j.procs.2024.09.664