A general method to the strong law of large numbers and its applications

作者：Yang, Shanchao^*; Su, Chun; Yu, Kerning

来源：Statistics & Probability Letters, 2008, 78(6): 794-803.

DOI：10.1016/j.spl.2007.09.046

• strong law of large numbers
• tail probability of maximal sums
• associated random variables
• rate of convergence

A general method to prove the strong law of large numbers is given by using the maximal tail probability. As a result the convergence rate of S-n/n for both positively associated sequences and negatively associated sequences is n(-1/2) (log n)(1/2)(log log n)(6/2) for any delta > 1. This result closes to the optimal achievable convergence rate under independent random variables, and improves the rates n(-1/3)(log n)(2/3) and n(-1/3)(log n)(5/3) obtained by loannides and Roussas [1099. Exponential inequality for associated random variables. Statist. Probab. Lett. 42, 423-431] and Oliveira [2005. An exponential inequality for associated variables. Statist. Probalb. Lett. 73, 189-197], respectively. In this sense the proposed general method may be more effective than its peers provided by Fazekas and Klesov [2001. A general approach to the strong law of large numbers. Theory Probab. Appl. 45(3), 436-449] and loannides and Roussas [1999. Exponential inequality for associated random variables. Statist. Probab. Lett. 42, 423-431].

• 出版日期2008-4-15
• 单位中国科学技术大学; 广西师范大学