On Stein factors in Stein's method for normal approximation

2024/10/07 by Gaunt, Robert E. · 2 citations
#60F05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2410.05475

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.

Cited by

• Stein's method for asymmetric Laplace approximation
• Operationalizing Stein's Method for Online Linear Optimization: CLT-Based Optimal Tradeoffs

Related

• Stein's method of normal approximation: Some recollections and reflections
• Multivariate Stein Factors for a Class of Strongly Log-concave Distributions
• Improved bounds in Stein's method for functions of multivariate normal random vectors
• New error bounds for Laplace approximation via Stein's method
• Testing normality in any dimension by Fourier methods in a multivariate Stein equation