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What is Learnable in Valiant's Theory of the Learnable? 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Hypothesis Test of a Truncated Sample Mean for the Extremely Heavy-Tailed Distributions
Tang Fuquan, Han Dong · 2021-12-06 · via math.ST updates on arXiv.org

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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