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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. 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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\""}]}, "item_6_select_64": {"attribute_name": "\u8457\u8005\u7248\u30d5\u30e9\u30b0", "attribute_value_mlt": [{"subitem_select_item": "author"}]}, "item_6_source_id_35": {"attribute_name": "ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "0378-3758", "subitem_source_identifier_type": "ISSN"}]}, "item_6_source_id_39": {"attribute_name": "NII ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "0378-3758", "subitem_source_identifier_type": "ISSN"}]}, "item_6_source_id_40": {"attribute_name": "\u66f8\u8a8c\u30ec\u30b3\u30fc\u30c9ID", "attribute_value_mlt": [{"subitem_source_identifier": "AA00253748", "subitem_source_identifier_type": "NCID"}]}, "item_6_text_69": {"attribute_name": "wosonly authkey", "attribute_value_mlt": [{"subitem_text_value": "Curved exponential family; Information loss; Fisher information metric; Embedding curvature; Affine connection; Positive definite matrix"}]}, "item_6_text_70": {"attribute_name": "wosonly keywords", "attribute_value_mlt": [{"subitem_text_value": "DIFFERENTIAL GEOMETRY; RIEMANNIAN GEOMETRY; LATENT ROOTS"}]}, "item_6_textarea_68": {"attribute_name": "wosonly abstract", "attribute_value_mlt": [{"subitem_textarea_value": "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. (C) 2014 Elsevier B.V. All rights reserved."}]}, "item_creator": {"attribute_name": "\u8457\u8005", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Sheena,  Yo"}], "nameIdentifiers": [{"nameIdentifier": "4158", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "\u30d5\u30a1\u30a4\u30eb\u60c5\u5831", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2015-09-24"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "Inference_on_the_eigenvalues.pdf", "filesize": [{"value": "184.6 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_note", "mimetype": "application/pdf", "size": 184600.0, "url": {"label": "Inference_on_the_eigenvalues.pdf", "url": "https://soar-ir.repo.nii.ac.jp/record/2615/files/Inference_on_the_eigenvalues.pdf"}, "version_id": "7d9730c7-5cf2-4d19-bd5f-209c212c0404"}]}, "item_keyword": {"attribute_name": "\u30ad\u30fc\u30ef\u30fc\u30c9", "attribute_value_mlt": [{"subitem_subject": "Curved exponential family", "subitem_subject_scheme": "Other"}, {"subitem_subject": "Information loss", "subitem_subject_scheme": "Other"}, {"subitem_subject": "Fisher information metric", "subitem_subject_scheme": "Other"}, {"subitem_subject": "Embedding curvature", "subitem_subject_scheme": "Other"}, {"subitem_subject": "Affine connection", "subitem_subject_scheme": "Other"}, {"subitem_subject": "Positive definite matrix", "subitem_subject_scheme": "Other"}]}, "item_language": {"attribute_name": "\u8a00\u8a9e", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"resourcetype": "journal article", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "Inference on the eigenvalues of the covariance matrix of a multivariate normal distribution\u2014Geometrical view", "item_titles": {"attribute_name": "\u30bf\u30a4\u30c8\u30eb", "attribute_value_mlt": [{"subitem_title": "Inference on the eigenvalues of the covariance matrix of a multivariate normal distribution\u2014Geometrical view", "subitem_title_language": "en"}]}, "item_type_id": "6", "owner": "1", "path": ["310/311"], "permalink_uri": "http://hdl.handle.net/10091/18065", "pubdate": {"attribute_name": "PubDate", "attribute_value": "2015-02-02"}, "publish_date": "2015-02-02", "publish_status": "0", "recid": "2615", "relation": {}, "relation_version_is_last": true, "title": ["Inference on the eigenvalues of the covariance matrix of a multivariate normal distribution\u2014Geometrical view"], "weko_shared_id": -1}