Sankhya: The Indian Journal of Statistics

2006, Volume 68, Pt. 1, 24--44

Chover's Law of the Iterated Logarithm for Weighted Sums with Application

Pingyan Chen, Jinan University, Guangzhou, PR China
Yongcheng Qi, University of Minnesota Duluth, Duluth, USA

SUMMARY. Consider weighted sums of independent variables with a common  distribution function  in the domain of attraction of a stable law. Peng and Qi (2003) established the Chover-type law of the iterated logarithm.  This paper extends the law to a larger class of weighted sums. As an application, it is shown that the Chover-type law of the iterated logarithm for products of sums holds when the  underlying distribution is in the domain of attraction of a stable law with an exponent larger than one.

AMS (1991) subject classification. Primary 60F15.

Key words and phrases. Weighted sums, product of sums, law of iterated logarithm, stable laws , domain of attraction.

Full paper (PDF)