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NON-UNIFORM ESTIMATES IN THE CENTRAL LIMIT THEOREM FOR RANDOM SUMS OF INDEPENDENT RANDOM VARIABLES
http://hdl.handle.net/10131/5575
http://hdl.handle.net/10131/557510361f64-fbac-4593-91c4-a2d03c7d2ec0
名前 / ファイル | ライセンス | アクション |
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YMJ_37_N1_1989_061-076.pdf (1.2 MB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2009-12-15 | |||||
タイトル | ||||||
タイトル | NON-UNIFORM ESTIMATES IN THE CENTRAL LIMIT THEOREM FOR RANDOM SUMS OF INDEPENDENT RANDOM VARIABLES | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
著者 |
Fotopoulos, S. B.
× Fotopoulos, S. B. |
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著者所属 | ||||||
Department of Management and Systems, Washington State University, Pullman, WA 99164, U. S. A | ||||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | 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$ . | |||||
書誌情報 |
Yokohama Mathematical Journal = 横濱市立大學紀要. D部門, 数学 巻 37, 号 1, p. 61-76, 発行日 1989 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 00440523 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA0089285X | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
出版者 | ||||||
出版者 | Yokohama City University |