On Stein factors in Stein's method for normal approximation

Robert Gaunt

doi:10.1016/j.spl.2024.110339

On Stein factors in Stein's method for normal approximation

Robert Gaunt

Probability

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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.

Original language	English
Article number	110339
Journal	Statistics & Probability Letters
Volume	219
Early online date	14 Dec 2024
DOIs	https://doi.org/10.1016/j.spl.2024.110339
Publication status	Published - 1 Apr 2025

Keywords

Stein’s method
Stein equation
normal distribution
AMS 2010 Subject Classification: Primary 60F05

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10.1016/j.spl.2024.110339Licence: CC BY

2410.05475v1Submitted manuscript, 110 KB

Cite this

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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. ",

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AB - 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.

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KW - Stein equation

KW - normal distribution

KW - AMS 2010 Subject Classification: Primary 60F05

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DO - 10.1016/j.spl.2024.110339

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JO - Statistics & Probability Letters

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ER -

On Stein factors in Stein's method for normal approximation

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

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On Stein factors in Stein's method for normal approximation

Abstract

Keywords

Access to Document

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

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