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  1. 030 経法学部, 経済学部, 大学院経済・社会政策科学研究科
  2. 0301 学術論文

Inference on the eigenvalues of the covariance matrix of a multivariate normal distribution—Geometrical view

http://hdl.handle.net/10091/18065
http://hdl.handle.net/10091/18065
a8d188ca-579c-4f72-913e-df67260fbdc5
名前 / ファイル ライセンス アクション
Inference_on_the_eigenvalues.pdf Inference_on_the_eigenvalues.pdf (184.6 kB)
Item type 学術雑誌論文 / Journal Article(1)
公開日 2015-02-02
タイトル
タイトル Inference on the eigenvalues of the covariance matrix of a multivariate normal distribution—Geometrical view
言語
言語 eng
DOI
関連識別子 https://doi.org/10.1016/j.jspi.2014.03.004
関連名称 10.1016/j.jspi.2014.03.004
キーワード
主題 Curved exponential family, Information loss, Fisher information metric, Embedding curvature, Affine connection, Positive definite matrix
資源タイプ
資源 http://purl.org/coar/resource_type/c_6501
タイプ journal article
著者 Sheena, Yo

× Sheena, Yo

Sheena, Yo

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出版者
出版者 ELSEVIER SCIENCE BV
引用
内容記述 JOURNAL OF STATISTICAL PLANNING AND INFERENCE.150:66-83 (2014)
書誌情報 JOURNAL OF STATISTICAL PLANNING AND INFERENCE

巻 150, p. 66-83, 発行日 2014-07
抄録
内容記述 We consider inference on the eigenvalues of the covariance matrix of a multivariate normal distribution. The family of multivariate normal distributions with a fixed mean is seen as a Riemannian manifold with Fisher information metric. Two submanifolds naturally arises: one is the submanifold given by the fixed eigenvectors of the covariance matrix; the other is the one given by the fixed eigenvalues. We analyze the geometrical structures of these manifolds such as metric, embedding curvature under e-connection or m-connection. Based on these results, we study (1) the bias of the sample eigenvalues, (2) the asymptotic variance of estimators, (3) the asymptotic information loss caused by neglecting the sample eigenvectors, (4) the derivation of a new estimator that is natural from a geometrical point of view.
資源タイプ(コンテンツの種類)
ISSN
収録物識別子タイプ ISSN
収録物識別子 0378-3758
書誌レコードID
収録物識別子タイプ NCID
収録物識別子 AA00253748
権利
権利情報 © 2014 Elsevier B.V. "NOTICE: this is the author’s version of a work that was accepted for publication in JOURNAL OF STATISTICAL PLANNING AND INFERENCE. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in PUBLICATION, [VOL 150, (7, 2014)] DOI:10.1016/j.jspi.2014.03.004"
出版タイプ
出版タイプ AM
出版タイプResource http://purl.org/coar/version/c_ab4af688f83e57aa
WoS
URL http://gateway.isiknowledge.com/gateway/Gateway.cgi?&GWVersion=2&SrcAuth=ShinshuUniv&SrcApp=ShinshuUniv&DestLinkType=FullRecord&DestApp=WOS&KeyUT=000337773900004
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Cite as

Sheena, Yo, 2014, Inference on the eigenvalues of the covariance matrix of a multivariate normal distribution—Geometrical view: ELSEVIER SCIENCE BV, 66–83 p.

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