具有胖尾的独立随机变量中二次型的概率和矩不等式

Pub Date : 2024-10-28 DOI:10.1016/j.spl.2024.110290

Chi Zhang, Danna Zhang

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引用次数: 0

摘要

二次型的概率不等式和矩不等式是研究二阶统计特性的重要工具。关于具有有限指数矩的随机变量中的二次型，已有大量结果。然而，允许较弱矩条件的对应结果并不充分。在这项研究中，我们提出了一个新的纳加耶夫型尾概率不等式和一个罗森塔尔型矩不等式，用于具有肥尾的随机变量中的二次型。

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Probability and moment inequalities for quadratic forms in independent random variables with fat tails

Probability and moment inequalities for quadratic forms are valuable tools in studying the properties of second-order statistics. There are extensive results regarding quadratic forms in random variables with finite exponential moments. However, the counterpart that allows for weaker moment conditions is inadequate. In this work, we present a new Nagaev-type tail probability inequality and a Rosenthal-type moment inequality for quadratic forms in random variables with fat tails.

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