Hypothesis Test of a Truncated Sample Mean for the Extremely Heavy-Tailed Distributions

Tang Fuquan; Han Dong

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arXiv · 2112.02742

Hypothesis Test of a Truncated Sample Mean for the Extremely Heavy-Tailed Distributions

Tang Fuquan·Han Dong

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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.

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Tang Fuquan, Han Dong. 2021-12-06. Hypothesis Test of a Truncated Sample Mean for the Extremely Heavy-Tailed Distributions. https://arxiv.org/abs/2112.02742

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