Theoretical Statistics and Mathematics Unit, ISI Delhi

February 22, 2012 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Arijit Chakrabarty,
Indian Statistical Institute, Delhi

Title:
Large deviations for truncated heavy-tailed random variables: a boundary case

Abstract of Talk

Suppose that $X_1,X_2,\ldots$ are i.i.d. random variables with regularly varying tails, and $(M_n)$ is deterministic sequence going to infinity. In this talk, we shall study the decay rate of $P(S_n > kM_n)$ where $k$ is a positive integer, and
\[
S_n:=\sum_{j=1}^n X_j {\bf 1}(|X_j|\le M_n)\,.
\]
It turns out that the case when $k$ is an integer is very different from that when it is not so, from the points of view of the decay rate and its proof. The reason for this difference, and the method of attack for the above mentioned problem are the content of this talk.