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Consistency of an Information Criterion for High-dimensional Multivariate Regression (Paperback)

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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 8 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 thatn goes to 8 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.

Genre: Mathematics, Computers + Internet, Social Science
Series Title: Jss Research: Statistics
Format: Paperback
Publisher: Springer Verlag
Author: Hirokazu Yanagihara
Language: English
Street Date: April 8, 2017
TCIN: 51941350
UPC: 9784431557746
Item Number (DPCI): 248-37-3232

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