Higher-order Stein kernels for Gaussian approximation
Tom 256 / 2021
Studia Mathematica 256 (2021), 241-258
MSC: Primary 60F05; Secondary 60E15, 26D10, 94A17.
DOI: 10.4064/sm190415-28-10
Opublikowany online: 6 July 2020
Streszczenie
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.
