Authors:
- 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
Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)
Part of the book sub series: JSS Research Series in Statistics (JSSRES)
About this book
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.
Keywords
- Consistency
- High-dimensional Asymptotics
- Information Criterion
- Nonnormality
- Variable Selection
Authors and Affiliations
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Hiroshima University, Higashi-Hiroshima, Japan
Hirokazu Yanagihara
Bibliographic Information
Book Title: Consistency of an Information Criterion for High-Dimensional Multivariate Regression
Authors: Hirokazu Yanagihara
Series Title: SpringerBriefs in Statistics
Publisher: Springer Tokyo
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive licence to Springer Japan KK 2024
Softcover ISBN: 978-4-431-55774-6Due: 23 July 2024
eBook ISBN: 978-4-431-55775-3Due: 23 July 2024
Series ISSN: 2191-544X
Series E-ISSN: 2191-5458
Edition Number: 1
Number of Pages: X, 60