Stein operators, kernels and discrepancies for multivariate continuous distributions

Abstract : We present a general framework for setting up Stein's method for multivariate continuous distributions. The approach gives a collection of Stein characterizations, among which we highlight score-Stein operators and kernel-Stein operators. Applications include copu-las and distance between posterior distributions. We give a general explicit 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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Submitted on : Friday, December 20, 2019 - 10:39:06 AM
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Guillaume Mijoule, Gesine Reinert, Yvik Swan. Stein operators, kernels and discrepancies for multivariate continuous distributions. 2019. ⟨hal-02420874⟩

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