On strong laws of large numbers for arrays of rowwise independent random elements
Let {Xnk} be an array of rowwise independent random elements in a separable Banach space of type r, 1≤r≤2. Complete convergence of n1/p∑k=1nXnk to 0, 0<p<r≤2 is obtained when sup1≤k≤nE ‖Xnk‖v=O(nα), α≥0 with v(1p−1r)>α+1. An application to density estimation is also given....
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000729 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832550301122428928 |
|---|---|
| author | Abolghassem Bozorgnia Ronald Frank Patterson Robert Lee Taylor |
| author_facet | Abolghassem Bozorgnia Ronald Frank Patterson Robert Lee Taylor |
| author_sort | Abolghassem Bozorgnia |
| collection | DOAJ |
| description | Let {Xnk} be an array of rowwise independent random elements in a separable
Banach space of type r, 1≤r≤2. Complete convergence of n1/p∑k=1nXnk to 0,
0<p<r≤2 is obtained when sup1≤k≤nE ‖Xnk‖v=O(nα), α≥0 with
v(1p−1r)>α+1. An application to density estimation is also given. |
| format | Article |
| id | doaj-art-b9fdaff853364c4594db0cd37f2ff445 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b9fdaff853364c4594db0cd37f2ff4452025-02-03T06:07:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116358759110.1155/S0161171293000729On strong laws of large numbers for arrays of rowwise independent random elementsAbolghassem Bozorgnia0Ronald Frank Patterson1Robert Lee Taylor2Department of Statistics, Mashhad University, Mashhad, IranDepartment of Mathematics and Computer Science, Georgia State University, Atlanta, Ga 30303, USADepartment of Statistics, University of Georgia, Athens, Ga 30602, USALet {Xnk} be an array of rowwise independent random elements in a separable Banach space of type r, 1≤r≤2. Complete convergence of n1/p∑k=1nXnk to 0, 0<p<r≤2 is obtained when sup1≤k≤nE ‖Xnk‖v=O(nα), α≥0 with v(1p−1r)>α+1. An application to density estimation is also given.http://dx.doi.org/10.1155/S0161171293000729radom elementstrong laws of large numbercomplete convergenceRademacher r type space. |
| spellingShingle | Abolghassem Bozorgnia Ronald Frank Patterson Robert Lee Taylor On strong laws of large numbers for arrays of rowwise independent random elements International Journal of Mathematics and Mathematical Sciences radom element strong laws of large number complete convergence Rademacher r type space. |
| title | On strong laws of large numbers for arrays of rowwise independent random elements |
| title_full | On strong laws of large numbers for arrays of rowwise independent random elements |
| title_fullStr | On strong laws of large numbers for arrays of rowwise independent random elements |
| title_full_unstemmed | On strong laws of large numbers for arrays of rowwise independent random elements |
| title_short | On strong laws of large numbers for arrays of rowwise independent random elements |
| title_sort | on strong laws of large numbers for arrays of rowwise independent random elements |
| topic | radom element strong laws of large number complete convergence Rademacher r type space. |
| url | http://dx.doi.org/10.1155/S0161171293000729 |
| work_keys_str_mv | AT abolghassembozorgnia onstronglawsoflargenumbersforarraysofrowwiseindependentrandomelements AT ronaldfrankpatterson onstronglawsoflargenumbersforarraysofrowwiseindependentrandomelements AT robertleetaylor onstronglawsoflargenumbersforarraysofrowwiseindependentrandomelements |