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Stein equations; Stein's method; Stein factors; Kolmogorov distance; Wasserstein distance; Total variation distance; Integral probability metrics
Abstract :
[en] In this paper we provide a probabilistic representation of Lagrange’s identity which we
use to obtain Papathanasiou-type variance expansions of arbitrary order. Our expansions lead to generalized sequences of weights which depend on an arbitrarily chosen sequence of (non-decreasing) test functions. The expansions hold for univariate target distribution under weak assumptions, in particular they hold for continuous and lattice distributions alike. The weights are studied under different sets of assumptions either on the test functions or on the underlying distributions. Many concrete illustrations for standard probability distributions are provided (including Pearson, Ord, Laplace, Rayleigh, Cauchy, and Levy distributions).
Disciplines :
Mathematics
Author, co-author :
Ernst, Marie ; Université de Liège - ULiège > Département de mathématique > Département de mathématique
Swan, Yvik ; Université de Liège - ULiège > Département de mathématique > Probabilités et statistique mathématique
Reinert, Gesine; University of Oxford > Department of Statistics
Language :
English
Title :
On Papathanasiou’s covariance expansions
Publication date :
2022
Journal title :
ALEA: Latin American Journal of Probability and Mathematical Statistics
eISSN :
1980-0436
Publisher :
Instituto Nacional de Matematica Pura e Aplicada, Brazil
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