Exact lower bounds on the exponential moments of Winsorized and truncated random variables
Probability
2017-01-17 v1 Statistics Theory
Statistics Theory
Abstract
Exact lower bounds on the exponential moments of min(y,X) and XI{X<y} are provided given the first two moments of a random variable X. These bounds are useful in work on large deviations probabilities and nonuniform Berry-Esseen bounds, when the Cram\'er tilt transform may be employed. Asymptotic properties of these lower bounds are presented. Comparative advantages of the Winsorization min(y,X) over the truncation XI{X<y} are demonstrated.
Keywords
Cite
@article{arxiv.1001.2901,
title = {Exact lower bounds on the exponential moments of Winsorized and truncated random variables},
author = {Iosif Pinelis},
journal= {arXiv preprint arXiv:1001.2901},
year = {2017}
}