Name: On Stein factors in Stein’s method for normal approximation
Creator: Robert E. Gaunt
Keywords: normal distribution, 60F05, Probability (math.PR), FOS: Mathematics, Stein equation, Stein’s method, AMS 2010 Subject Classification: Primary 60F05, Mathematics - Probability

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Apr 2025Embargo end date: 01 Jan 2024 English Publisher:Elsevier BVJournal:Statistics & Probability Letters, volume 219, page 110,339 (issn: 0167-7152,

Authors: Robert E. Gaunt;

doi: 10.1016/j.spl.2024.110339 , 10.48550/arxiv.2410.05475

arXiv: http://arxiv.org/abs/2410.05475

On Stein factors in Stein’s method for normal approximation

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Abstract

Building on the rather large literature concerning the regularity of the solution of the standard normal Stein equation, we provide a complete description of the best possible uniform bounds for the derivatives of the solution of the standard normal Stein equation when the test functions belong to the class of real-valued functions whose $k$-th order derivative is Lipschitz.

4 pages

Related Organizations

University of Salford
United Kingdom

Keywords

normal distribution, 60F05, Probability (math.PR), FOS: Mathematics, Stein equation, Stein’s method, AMS 2010 Subject Classification: Primary 60F05, Mathematics - Probability

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UKRI| Rates of Convergence in Multivariate Normal Approximation by Stein's Method