Stein operators, kernels and discrepancies for multivariate continuous distributions

Guillaume Mijoule; Gesine Reinert; Yvik Swan

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arXiv · 1806.03478

Stein operators, kernels and discrepancies for multivariate continuous distributions

Guillaume Mijoule·Gesine Reinert·Yvik Swan

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Abstract

In this paper we present a general framework for Stein's method for multivariate continuous distributions. The approach gives a collection of Stein characterisations, among which we highlight score-Stein operators and kernel Stein operators. Applications include copulas and distance between posterior distributions. We give a general construction for Stein kernels for elliptical distributions and discuss Stein kernels in generality, highlighting connections with Fisher information and mass transport. Finally, a goodness-of-fit test based on Stein discrepancies is given.

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Guillaume Mijoule, Gesine Reinert, Yvik Swan. 2018-06-09. Stein operators, kernels and discrepancies for multivariate continuous distributions. https://arxiv.org/abs/1806.03478

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