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.
ISBN: | 9784431557746 |
Publication date: | 23rd July 2024 |
Author: | Hirokazu Yanagihara |
Publisher: | Springer an imprint of Springer Japan |
Format: | Paperback |
Pagination: | 60 pages |
Series: | SpringerBriefs in Statistics |
Genres: |
Probability and statistics Social research and statistics Mathematical and statistical software Economics, Finance, Business and Management |