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

Shanchao Yang, Chun Su and Keming Yu

Statistics & Probability Letters, 2008, vol. 78, issue 6, 794-803

Abstract: 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 Sn/n for both positively associated sequences and negatively associated sequences is for any [delta]>1. This result closes to the optimal achievable convergence rate under independent random variables, and improves the rates n-1/3(logn)2/3 and n-1/3(logn)5/3 obtained by Ioannides and Roussas [1999. Exponential inequality for associated random variables. Statist. Probab. Lett. 42, 423-431] and Oliveira [2005. An exponential inequality for associated variables. Statist. Probab. 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 Ioannides and Roussas [1999. Exponential inequality for associated random variables. Statist. Probab. Lett. 42, 423-431].

Keywords: Strong; law; of; large; numbers; Tail; probability; of; maximal; sums; Associated; random; variable; Rate; of; convergence (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00334-3
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:78:y:2008:i:6:p:794-803

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().