On Stein factors in Stein's method for normal approximation

Robert Gaunt

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
Journal	Statistics & Probability Letters
Publication status	Accepted/In press - 8 Dec 2024

Keywords

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

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2410.05475v1Submitted manuscript, 110 KB

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normal_Stein_equation_fv
Accepted author manuscript, 247 KB
Licence: CC BY
Embargo ends: 9/12/25

Cite this

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title = "On Stein factors in Stein's method for normal approximation",

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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author = "Robert Gaunt",

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language = "English",

journal = "Statistics & Probability Letters",

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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

M3 - Article

SN - 0167-7152

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

ER -

On Stein factors in Stein's method for normal approximation

Abstract

Keywords

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