Consistency of an Information Criterion for High-Dimensional Multivariate Regression
Authors: Yanagihara, Hirokazu
- 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
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- 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.
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Consistency of an Information Criterion for High-Dimensional Multivariate Regression
- Authors
-
- Hirokazu Yanagihara
- Series Title
- JSS Research Series in Statistics
- Copyright
- 2021
- Publisher
- Springer Japan
- Copyright Holder
- The Author(s), under exclusive licence to Springer Japan KK
- eBook ISBN
- 978-4-431-55775-3
- Softcover ISBN
- 978-4-431-55774-6
- Series ISSN
- 2364-0057
- Edition Number
- 1
- Number of Pages
- X, 60
- Topics
