A note on symmetrization procedures for the laws of large numbers

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• 作者：Deli Li^a ; Han-Ying Liang^b ; ^{hyliang@tongji.edu.cn} ; Andrew Rosalsky^c
• 关键词：60F15 ; 60F05 ; 60B12 ; 60G50
• 刊名：Statistics & Probability Letters
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：121
• 期：Complete
• 页码：136-142
• 全文大小：386 K
• 卷排序：121

文摘

In this note, general symmetrization procedures for both the weak and strong laws of large numbers concerning the row sums from arrays of rowwise independent Banach space valued random variables are established. Necessary and sufficient conditions are provided for the weak and strong laws of large numbers to hold in terms of corresponding laws of large numbers for a symmetrized version of the array. Several corollaries of the main result are provided.