Variable Selection in Multivariate Linear Regression Models with Fewer Observations than the Dimension
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- Yamamura Mariko
- Department of Clinical Medicine (Biostatistics), School of Pharmacy, Kitasato University
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- Yanagihara Hirokazu
- Department of Mathematics, Graduate School of Science, Hiroshima University
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- Srivastava Muni S.
- Department of Statistics, University of Toronto
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Abstract
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 ∞ simultaneously. By conducting numerical studies, we verify that our new criteria perform well.
Journal
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- Ouyou toukeigaku
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Ouyou toukeigaku 39 (1), 1-19, 2010
Japanese Society of Applied Statistics
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Keywords
Details 詳細情報について
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- CRID
- 1390001204443184256
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- NII Article ID
- 10026049107
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- NII Book ID
- AN00330942
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- ISSN
- 18838081
- 02850370
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- NDL BIB ID
- 10674088
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed