Sankhya: The Indian Journal of Statistics

2006, Volume 68, Pt. 3, 461--487

Chover's Law of the Iterated Logarithm for Trimmed Sums

Xuewen Lu, University of Calgary, Calgary, Canada
Yongcheng Qi, University of Minnesota, Duluth, USA

SUMMARY. In this paper, we deal with sequences of exchangeable observations, which are conditionally independent and identically distributed with a common (random) distribution $\tau$, where $\tau$ is defined by the conditioning of a normalized random measure with independent increments. By application of a multidimensional version of the Faàa di Bruno formula, we derive explicit closed form expressions for the finite dimensional distributions and the predictive distributions of the sequence. The results are illustrated through suitable examples.

AMS (2000) subject classification. Primary 60F15.

Key words and phrases. Trimmed sum, law of the iterated logarithm, stable law, domain of attraction.

Full paper (PDF)