Hypothesis Test of a Truncated Sample Mean for the Extremely Heavy-Tailed Distributions
Statistics Theory
2021-12-07 v1 Applications
Statistics Theory
Abstract
This article deals with the hypothesis test for the extremely heavy-tailed distributions with infinite mean or variance by using a truncated sample mean. We obtain three necessary and sufficient conditions under which the asymptotic distribution of the truncated test statistics converges to normal, neither normal nor stable or converges to or the combination of stable distributions, respectively. The numerical simulation illustrates an application of the theoretical results above in the hypothesis testing.
Keywords
Cite
@article{arxiv.2112.02742,
title = {Hypothesis Test of a Truncated Sample Mean for the Extremely Heavy-Tailed Distributions},
author = {Tang Fuquan and Han Dong},
journal= {arXiv preprint arXiv:2112.02742},
year = {2021}
}