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2018 Stein approximation for functionals of independent random sequences
Nicolas Privault, Grzegorz Serafin
Electron. J. Probab. 23: 1-34 (2018). DOI: 10.1214/17-EJP132

Abstract

We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and functionals of both continuous and discrete independent random variables. For random variables admitting a continuous density, it recovers classical distance bounds based on absolute third moments, with better and explicit constants. We also apply this method to multiple stochastic integrals that can be used to represent $U$-statistics, and include linear and quadratic functionals as particular cases.

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Nicolas Privault. Grzegorz Serafin. "Stein approximation for functionals of independent random sequences." Electron. J. Probab. 23 1 - 34, 2018. https://doi.org/10.1214/17-EJP132

Information

Received: 7 April 2017; Accepted: 26 December 2017; Published: 2018
First available in Project Euclid: 31 January 2018

zbMATH: 1390.60093
MathSciNet: MR3761564
Digital Object Identifier: 10.1214/17-EJP132

Subjects:
Primary: 60F05, 60G57, 60H07

JOURNAL ARTICLE
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Vol.23 • 2018
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