{"created":"2021-03-01T07:02:04.081220+00:00","id":42210,"links":{},"metadata":{"_buckets":{"deposit":"712e0aa9-d473-4c68-a609-d3c710cd3eac"},"_deposit":{"id":"42210","owners":[],"pid":{"revision_id":0,"type":"depid","value":"42210"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00042210","sets":["62:7433:7434","9:7435:7436"]},"item_8_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2012-07","bibliographicIssueDateType":"Issued"},"bibliographicVolumeNumber":"CIRJE-F-855","bibliographic_titles":[{"bibliographic_title":"Discussion paper series. CIRJE-F"}]}]},"item_8_description_13":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_8_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"The problem of estimating covariance and precision matrices of multivariate normal distributions is addressed when both the sample size and the dimension of variables are large. The estimation of the precision matrix is important in various statistical inference including the Fisher linear discriminant analysis, confidence region based on the Mahalanobis distance and others. A standard estimator is the inverse of the sample covariance matrix, but it may be instable or can not be defined in the high dimension. Although (adaptive) ridge type estimators are alternative procedures which are useful and stable for large dimension. However, we are faced with questions about how to choose ridge parameters and their estimators and how to set up asymptotic order in ridge functions in high dimensional cases. In this paper, we consider general types of ridge estimators for covariance and precision matrices, and derive asymptotic expansions of their risk functions. Then we suggest the ridge functions so that the second order terms of risks of ridge estimators are smaller than those of risks of the standard estimators.","subitem_description_type":"Abstract"}]},"item_8_description_6":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"本文フィルはリンク先を参照のこと","subitem_description_type":"Other"}]},"item_8_publisher_20":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"日本経済国際共同センター"}]},"item_8_relation_25":{"attribute_name":"関係URI","attribute_value_mlt":[{"subitem_relation_type_id":{"subitem_relation_type_id_text":"http://www.cirje.e.u-tokyo.ac.jp/research/dp/2012/2012cf855ab.html","subitem_relation_type_select":"URI"}}]},"item_8_source_id_10":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA11450569","subitem_source_identifier_type":"NCID"}]},"item_8_subject_15":{"attribute_name":"日本十進分類法","attribute_value_mlt":[{"subitem_subject":"335","subitem_subject_scheme":"NDC"}]},"item_8_text_21":{"attribute_name":"出版者別名","attribute_value_mlt":[{"subitem_text_value":"Center for International Research on the Japanese Economy"}]},"item_8_text_4":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Department of Economics, University of Tokyo"},{"subitem_text_value":"Graduate School of Economics, University of Tokyo"}]},"item_access_right":{"attribute_name":"アクセス権","attribute_value_mlt":[{"subitem_access_right":"metadata only access","subitem_access_right_uri":"http://purl.org/coar/access_right/c_14cb"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Kubokawa, Tatsuya"}],"nameIdentifiers":[{"nameIdentifier":"97150","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"Inoue, Akira"}],"nameIdentifiers":[{"nameIdentifier":"97151","nameIdentifierScheme":"WEKO"}]}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Asymptotic expansion","subitem_subject_scheme":"Other"},{"subitem_subject":"covariance matrix","subitem_subject_scheme":"Other"},{"subitem_subject":"high dimension","subitem_subject_scheme":"Other"},{"subitem_subject":"Moore-Penrose inverse","subitem_subject_scheme":"Other"},{"subitem_subject":"multivariate normal distribution","subitem_subject_scheme":"Other"},{"subitem_subject":"point estimation","subitem_subject_scheme":"Other"},{"subitem_subject":"precision matrix","subitem_subject_scheme":"Other"},{"subitem_subject":"ridge estimator","subitem_subject_scheme":"Other"},{"subitem_subject":"risk comparison","subitem_subject_scheme":"Other"},{"subitem_subject":"Stein-Haff identity","subitem_subject_scheme":"Other"},{"subitem_subject":"Stein loss","subitem_subject_scheme":"Other"},{"subitem_subject":"Wishart distribution","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"technical report","resourceuri":"http://purl.org/coar/resource_type/c_18gh"}]},"item_title":"Estimation of Covariance and Precision Matrices in High Dimension","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Estimation of Covariance and Precision Matrices in High Dimension"}]},"item_type_id":"8","owner":"1","path":["7436","7434"],"pubdate":{"attribute_name":"公開日","attribute_value":"2013-05-31"},"publish_date":"2013-05-31","publish_status":"0","recid":"42210","relation_version_is_last":true,"title":["Estimation of Covariance and Precision Matrices in High Dimension"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:17:26.223569+00:00"}