Hirokazu Yanagihara

Consistency of an Information Criterion for High-Dimensional Multivariate Regression

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• SpringerBriefs in Statistics
• Verlag: Springer / Springer Japan / Springer, Berlin
• Artikelnr. des Verlages: 978-4-431-55774-6
• 1st ed. 2024
• Seitenzahl: 60
• Erscheinungstermin: 23. Juli 2024
• Englisch
• Abmessung: 235mm x 155mm
• ISBN-13: 9784431557746
• ISBN-10: 4431557741
• Artikelnr.: 43298332

Inhaltsangabe

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.