Higher-order Stein kernels for Gaussian approximation
Résumé
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.
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