The heavy-tail behavior of the difference of two dependent random variables

Yiqing Chen

Statistics & Probability Letters, 2025, vol. 218, issue C

Abstract: Consider Z=X−Y, the difference of two nonnegative dependent random variables. We investigate how the difference Z inherits the heavy tail property of the minuend X and is altered by the subtrahend Y. In the case where X and Y are tail independent, we prove that if X has a long tail F¯X=1−FX, the asymptotic behavior of F¯X is exactly inherited by Z, that is, F¯Z∼F¯X, regardless of the tail behavior of Y. However, this result may not hold when X and Y exhibit tail dependence. Within the framework of bivariate regular variation, we show that the limit of the ratio F¯ZF¯X can range over the closed interval [0,1].

Keywords: Asymptotic equivalence; Long tail; Difference; Tail (in)dependence; Bivariate regular variation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2024.110307

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