A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Higher-order Stein kernels for Gaussian approximation

Volume 256 / 2021

Max Fathi Studia Mathematica 256 (2021), 241-258 MSC: Primary 60F05; Secondary 60E15, 26D10, 94A17. DOI: 10.4064/sm190415-28-10 Published online: 6 July 2020

Abstract

We introduce higher-order Stein kernels relative to the standard Gaussian measure, which generalize the usual Stein kernels by involving higher-order derivatives of test functions. We relate the associated discrepancies to various metrics on the space of probability measures and prove new functional inequalities involving them. As an application, we obtain new explicit improved rates of convergence in the classical multidimensional CLT under higher moment and regularity assumptions.

Authors

  • Max FathiCNRS & Institut de Mathématiques de Toulouse
    Université de Toulouse
    118 route de Narbonne
    31068 Toulouse, France
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image