On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements with application to moving average processes
AbstractWe obtain complete convergence results for arrays of rowwise independent Banach space valued random elements. In the main result no assumptions are made concerning the geometry of the underlying Banach space. As corollaries we obtain a result on complete convergence in stable type p Banach spaces and on the complete convergence of moving average processes.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 58 (2002)
Issue (Month): 2 (June)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Burton, Robert M. & Dehling, Herold, 1990. "Large deviations for some weakly dependent random processes," Statistics & Probability Letters, Elsevier, vol. 9(5), pages 397-401, May.
- Li, Deli & Bhaskara Rao, M. & Wang, Xiangchen, 1992. "Complete convergence of moving average processes," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 111-114, May.
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- Tómács, Tibor, 2005. "Convergence rates in the law of large numbers for arrays of Banach space valued random elements," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 59-69, April.
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