A Remark on Strong Law of Large Numbers for Weighted U-Statistics
DC Field | Value | Language |
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dc.contributor.author | Ha, Hyung-Tae | - |
dc.contributor.author | Huang, Mei Ling | - |
dc.contributor.author | Li, De Li | - |
dc.date.available | 2020-02-28T16:43:49Z | - |
dc.date.created | 2020-02-06 | - |
dc.date.issued | 2014-09 | - |
dc.identifier.issn | 1439-8516 | - |
dc.identifier.uri | https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/12328 | - |
dc.description.abstract | Let {X, X-n; n >= 1} be a sequence of i.i.d. random variables with values in a measurable space (5, S) such that E vertical bar h(X-1, X-2, ..., X-m)vertical bar < infinity, where h is a measurable symmetric function from S-m. into R = (-infinity, infinity). Let {w(n,i1,i2, ..., im); 1 <= i(1) < i(2) < ... < i(m) <= n, n >= m} be a matrix array of real numbers. Motivated by a result of Choi and Sung (1987), in this note we are concerned with establishing a strong law of large numbers for weighted U-statistics with kernel h of degree m. We show that [GRAPHICS] whenever sup(n >= m) max(1 <= i1 < i2 < ... < im <= n) vertical bar w(n,i1,i2, ..., im)vertical bar < infinity, where theta = Eh(X-1, X-2, ..., X-m). The proof of this result is based on a new general result on complete convergence, which is a fundamental tool, for array of real-valued random variables under some mild conditions. | - |
dc.language | 영어 | - |
dc.language.iso | en | - |
dc.publisher | SPRINGER HEIDELBERG | - |
dc.relation.isPartOf | ACTA MATHEMATICA SINICA-ENGLISH SERIES | - |
dc.subject | RANDOM-VARIABLES | - |
dc.subject | ASYMPTOTIC DISTRIBUTIONS | - |
dc.subject | SURE CONVERGENCE | - |
dc.subject | SUMS | - |
dc.subject | BEHAVIOR | - |
dc.title | A Remark on Strong Law of Large Numbers for Weighted U-Statistics | - |
dc.type | Article | - |
dc.type.rims | ART | - |
dc.description.journalClass | 1 | - |
dc.identifier.wosid | 000340351800011 | - |
dc.identifier.doi | 10.1007/s10114-014-1601-5 | - |
dc.identifier.bibliographicCitation | ACTA MATHEMATICA SINICA-ENGLISH SERIES, v.30, no.9, pp.1595 - 1605 | - |
dc.identifier.scopusid | 2-s2.0-84905678409 | - |
dc.citation.endPage | 1605 | - |
dc.citation.startPage | 1595 | - |
dc.citation.title | ACTA MATHEMATICA SINICA-ENGLISH SERIES | - |
dc.citation.volume | 30 | - |
dc.citation.number | 9 | - |
dc.contributor.affiliatedAuthor | Ha, Hyung-Tae | - |
dc.type.docType | Article | - |
dc.subject.keywordAuthor | Strong law of large numbers | - |
dc.subject.keywordAuthor | weighted U-statistics | - |
dc.subject.keywordAuthor | complete convergence | - |
dc.subject.keywordPlus | RANDOM-VARIABLES | - |
dc.subject.keywordPlus | ASYMPTOTIC DISTRIBUTIONS | - |
dc.subject.keywordPlus | SURE CONVERGENCE | - |
dc.subject.keywordPlus | SUMS | - |
dc.subject.keywordPlus | BEHAVIOR | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
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