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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 -\infty 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}
}