Theoretical Statistics and Mathematics Unit, ISI Delhi

Effect of truncation on large deviations for heavy-tailed random vectors

by Arijit Chakrabarty

This paper studies the effect of truncation on the large deviations behavior of the partial sum of a triangular array coming from a truncated power law model.
Each row of the triangular array consists of i.i.d. random vectors, whose distribution matches a power law on a ball of radius going to infinity, and outside that it has a light-tailed modification. The random vectors are assumed to be
$\mathbb{R}^d$-valued. It turns out that there are two regimes depending
on the growth rate of the truncating threshold, so that in one
regime, much of the heavy tailedness is retained, while in the
other regime, the same is lost.

isid/ms/2011/14 [fulltext]

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