## アブストラクト

Variable Selection in Multivariate Linear Regression Models with Fewer
Observations than the Dimension,1-19

Mariko Yamamura，Hirokazu Yanagihara and Muni S.Srivastava

英文要旨

This paper deals with the selection of variables in multivariate linear
regression models with fewer observations than the dimension by using Akaike's
information criterion (AIC). It is well known that the AIC cannot be defined
when the dimension of an observation is larger than the sample size, since an
ordinary estimator of the covariance matrix becomes singular. By replacing the
ordinary estimator of the covariance matrix with its ridge-type estimator, we
propose a new AIC for selecting variables of multivariate linear regression
models even though the dimension of an observation is larger than the sample
size. The bias correction term of AIC is evaluated from a remarkable asymptotic
theory based on the dimension and the sample size approaching to infinity
simultaneously. By conducting numerical studies, we verify that our new criteria
perform well.

「2010年第39巻 No.1」目次へ
「応用統計学」総目次へ

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