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- Hyodo Masashi
- Faculty of Science, Tokyo University of Science
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- Watanabe Hiroki
- Graduate School of Science, Tokyo University of Science
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- Nishiyama Takahiro
- School of Business Administration, Senshu University
Bibliographic Information
- Other Title
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- 共分散行列の逆行列の不偏推定量の改良
- キョウ ブンサン ギョウレツ ノ ギャクギョウレツ ノ フヘン スイテイリョウ ノ カイリョウ
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Abstract
In this paper, we consider the estimation of inverse of the covariance matrix. The estimation of the inverse of the covariance matrix under a multivariate normal distribution is an important issue in practical situations as well as from theoretical aspects. When the dimension is larger than the sample size, the Wishart matrix is singular, and thus many estimators have been constructed by using regularized estimation of the Wishart matrix. On the other hand, even if sample size is larger than dimension, it is well known that the usual estimator is typically not well-conditioned for the case dimension is large. In such situations, we propose the new estimators based on the unbiased estimator of the inverse of the covariance matrix. Also, the asymptotic optimalities with respect to loss for these estimators are obtained. Finally, the performances of our estimators are investigated by Monte Carlo simulations.
Journal
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- Bulletin of the Computational Statistics of Japan
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Bulletin of the Computational Statistics of Japan 28 (1), 3-17, 2015
Japanese Society of Computational Statistics
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Details 詳細情報について
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- CRID
- 1390282679357835264
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- NII Article ID
- 130005631730
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- NII Book ID
- AN10195854
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- ISSN
- 21899789
- 09148930
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- NDL BIB ID
- 026598401
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- CiNii Articles
- KAKEN
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- Abstract License Flag
- Disallowed