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Multivariate Stein factors for a class of strongly log-concave distributions. (English) Zbl 1348.60116
Electron. Commun. Probab. 21, Paper No. 56, 14 p. (2016); corrigendum ibid. 21, Paper No. 80, 2 p. (2016).
Summary: We establish uniform bounds on the low-order derivatives of Stein equation solutions for a broad class of multivariate, strongly log-concave target distributions. These “Stein factor” bounds deliver control over Wasserstein and related smooth function distances and are well-suited to analyzing the computable Stein discrepancy measures of Gorham and Mackey. Our arguments of proof are probabilistic and feature the synchronous coupling of multiple overdamped Langevin diffusions.

MSC:
60J60 Diffusion processes
62E17 Approximations to statistical distributions (nonasymptotic)
60E15 Inequalities; stochastic orderings
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