One more on the convergence rates in precise asymptotics

L.V. Rozovsky

Statistics & Probability Letters, 2021, vol. 171, issue C

Abstract: Let ηn,n≥1, be a sequence of random variables. We study conditions under which limε↘0∑n≥1ϕ(n)P(ηn≥f(εg(n)))−ν(ε)=C,where C is a constant, assuming among other conditions that non-negative functions ϕ(x) and f(x),g(x), tend, respectively, to 0 and to ∞ as x→∞. Results obtained, in particular, are wide generalization of the similar results obtained recently in Gut and Steinebach (2013), Kong (2016), Kong and Dai (2016) and Zhang (2019).

Keywords: Convergence rates; Precise asymptotics; Complete convergence (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2020.109023

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