Normal approximation and almost sure central limit theorem for non-symmetric Rademacher functionals

Guangqu Zheng

Stochastic Processes and their Applications, 2017, vol. 127, issue 5, 1622-1636

Abstract: In this work, we study the normal approximation and almost sure central limit theorems for some functionals of an independent sequence of Rademacher random variables. In particular, we provide a new chain rule that improves the one derived by Nourdin et al. (2010) and then we deduce the bound on Wasserstein distance for normal approximation using the (discrete) Malliavin–Stein approach. Besides, we are able to give the almost sure central limit theorem for a sequence of random variables inside a fixed Rademacher chaos using the Ibragimov–Lifshits criterion.

Keywords: Rademacher functional; Normal approximation; Wasserstein distance; Almost sure central limit theorem; Malliavin–Stein approach (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:5:p:1622-1636

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DOI: 10.1016/j.spa.2016.09.002

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