{"created":"2023-06-20T15:10:35.221817+00:00","id":6804,"links":{},"metadata":{"_buckets":{"deposit":"46b98964-a2e1-41e6-8589-c6b8babe6f5a"},"_deposit":{"created_by":3,"id":"6804","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"6804"},"status":"published"},"_oai":{"id":"oai:ynu.repo.nii.ac.jp:00006804","sets":["616:627:655"]},"author_link":["29694"],"item_6_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1989","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"1","bibliographicPageEnd":"76","bibliographicPageStart":"61","bibliographicVolumeNumber":"37","bibliographic_titles":[{"bibliographic_title":"Yokohama Mathematical Journal = 横濱市立大學紀要. D部門, 数学"}]}]},"item_6_description_17":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_6_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"Let ＄￥{X_{n}, n￥in N￥}＄ be a sequence of independent random variables with ＄E[X_{n}]=0＄ and ＄ E[X_{n}^{2}]<￥infty＄ , and let ＄￥{N_{n}, n￥in N￥}＄ be a sequence of random indices defined on the same space as ＄X_{n}' s＄ and independent of the latter. We write ＄S_{N_{n}}=￥sum_{i=}^{N_{n_{1}}}X_{i}＄ and ＄ L_{n}^{2}=Var(S_{N_{n}})<￥infty＄ . We show that for the validity ＄￥lim_{n￥rightarrow￥infty}￥Vert(1+|x|)^{2-1/p}|P(S_{N_{n}}￥leq L_{n}x)-￥Phi(x)|￥Vert_{p}=0＄ it is required that ￥lim_{n￥rightarrow￥infty}L_{n}^{-2-￥delta}E[￥Sigma_{i=1}^{N_{n}}E[|X_{i}|^{2+￥delta}]=0＄ for ＄ 1￥leq P￥leq￥infty＄ and ＄￥delta￥in(0,1)＄ , and ＄￥lim_{n￥rightarrow￥infty}L_{n}^{2-2}＄ . Var ＄(s_{N_{n}}^{2})^{1/2}=0＄ . Furthermore, we provide conditions under which the series ＄[￥Sigma_{n=1}^{￥infty}(g(L_{n})￥Vert(1+|x|)^{2-1/p}|P(S_{N_{n}}￥leq L_{n}x)-Phi(x)|￥Vert_{p})^{S}(t_{n}^{2}/L_{n}^{2})]^{1/S}＄ converges for any ＄ 1￥leq s<￥infty＄ .","subitem_description_type":"Abstract"}]},"item_6_publisher_35":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"Yokohama City University"}]},"item_6_source_id_11":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA0089285X","subitem_source_identifier_type":"NCID"}]},"item_6_source_id_9":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"00440523","subitem_source_identifier_type":"ISSN"}]},"item_6_text_4":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Department of Management and Systems, Washington State University, Pullman, WA 99164, U. S. A"}]},"item_6_version_type_18":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Fotopoulos, S. B."}],"nameIdentifiers":[{"nameIdentifier":"29694","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2016-09-26"}],"displaytype":"detail","filename":"YMJ_37_N1_1989_061-076.pdf","filesize":[{"value":"1.2 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"YMJ_37_N1_1989_061-076.pdf","url":"https://ynu.repo.nii.ac.jp/record/6804/files/YMJ_37_N1_1989_061-076.pdf"},"version_id":"8c639006-9d83-451e-b017-d370adfcbdee"}]},"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":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"NON-UNIFORM ESTIMATES IN THE CENTRAL LIMIT THEOREM FOR RANDOM SUMS OF INDEPENDENT RANDOM VARIABLES","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"NON-UNIFORM ESTIMATES IN THE CENTRAL LIMIT THEOREM FOR RANDOM SUMS OF INDEPENDENT RANDOM VARIABLES"}]},"item_type_id":"6","owner":"3","path":["655"],"pubdate":{"attribute_name":"公開日","attribute_value":"2009-12-15"},"publish_date":"2009-12-15","publish_status":"0","recid":"6804","relation_version_is_last":true,"title":["NON-UNIFORM ESTIMATES IN THE CENTRAL LIMIT THEOREM FOR RANDOM SUMS OF INDEPENDENT RANDOM VARIABLES"],"weko_creator_id":"3","weko_shared_id":3},"updated":"2023-06-20T18:40:02.058715+00:00"}