Strong laws of large numbers for arrays of row-wise exchangeable random elements
Let {Xnk,1≤k≤n,n≤1} be a triangular array of row-wise exchangeable random elements in a separable Banach space. The almost sure convergence of n−1/p∑k=1nXnk,1≤p<2, is obtained under varying moment and distribution conditions on the random elements. In particular, strong laws of large numbers foll...
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000126 |
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| _version_ | 1832564453442322432 |
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| author | Robert Lee Taylor Ronald Frank Patterson |
| author_facet | Robert Lee Taylor Ronald Frank Patterson |
| author_sort | Robert Lee Taylor |
| collection | DOAJ |
| description | Let {Xnk,1≤k≤n,n≤1} be a triangular array of row-wise exchangeable random elements in a separable Banach space. The almost sure convergence of n−1/p∑k=1nXnk,1≤p<2, is obtained under varying moment and distribution conditions on the random elements. In particular, strong laws of large numbers follow for triangular arrays of random elements in(Rademacher) type p separable Banach spaces. Consistency of the kernel density estimates can be obtained in this setting. |
| format | Article |
| id | doaj-art-1f1e949f344c41b2ad16f78fc5138005 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1f1e949f344c41b2ad16f78fc51380052025-02-03T01:10:52ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018113514410.1155/S0161171285000126Strong laws of large numbers for arrays of row-wise exchangeable random elementsRobert Lee Taylor0Ronald Frank Patterson1Department of Statistics and Computer Science, University of Georgia, Athens 30602, GA, USADepartment of Mathematics, Georgia State University, Atlanta 30303, GA, USALet {Xnk,1≤k≤n,n≤1} be a triangular array of row-wise exchangeable random elements in a separable Banach space. The almost sure convergence of n−1/p∑k=1nXnk,1≤p<2, is obtained under varying moment and distribution conditions on the random elements. In particular, strong laws of large numbers follow for triangular arrays of random elements in(Rademacher) type p separable Banach spaces. Consistency of the kernel density estimates can be obtained in this setting.http://dx.doi.org/10.1155/S0161171285000126exchangeabilityrandom elementslaws of large numbersalmost sure convergencemartingalesrademacher type pand Kernel density estimates. |
| spellingShingle | Robert Lee Taylor Ronald Frank Patterson Strong laws of large numbers for arrays of row-wise exchangeable random elements International Journal of Mathematics and Mathematical Sciences exchangeability random elements laws of large numbers almost sure convergence martingales rademacher type p and Kernel density estimates. |
| title | Strong laws of large numbers for arrays of row-wise exchangeable random elements |
| title_full | Strong laws of large numbers for arrays of row-wise exchangeable random elements |
| title_fullStr | Strong laws of large numbers for arrays of row-wise exchangeable random elements |
| title_full_unstemmed | Strong laws of large numbers for arrays of row-wise exchangeable random elements |
| title_short | Strong laws of large numbers for arrays of row-wise exchangeable random elements |
| title_sort | strong laws of large numbers for arrays of row wise exchangeable random elements |
| topic | exchangeability random elements laws of large numbers almost sure convergence martingales rademacher type p and Kernel density estimates. |
| url | http://dx.doi.org/10.1155/S0161171285000126 |
| work_keys_str_mv | AT robertleetaylor stronglawsoflargenumbersforarraysofrowwiseexchangeablerandomelements AT ronaldfrankpatterson stronglawsoflargenumbersforarraysofrowwiseexchangeablerandomelements |