Consistency of an Information Criterion for High-Dimensional Multivariate Regression
(Sprache: Englisch)
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...
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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.Inhaltsverzeichnis zu „Consistency of an Information Criterion for High-Dimensional Multivariate Regression “
1. Introduction.- 2. Information criteria in multivariate linear regression models.- 3.Several lemmas for proving consistency.- 4. Conditions to ensure consistency for AIC-type criterion under normality.- 5. Conditions to ensure consistency for AIC-type criterion under nonnormality.- 6. Conditions to ensure consistency of Cp-type criterion under normality.- 7. Conditions to ensure consistency of Cp-type criterion under nonnormality.- 8. Appendix.
Bibliographische Angaben
- Autor: Hirokazu Yanagihara
- 2024, 1st ed. 2024, X, 60 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 4431557741
- ISBN-13: 9784431557746
- Erscheinungsdatum: 16.09.2019
Sprache:
Englisch
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