TY - JOUR UR - http://lib.ugent.be/catalog/pug01:8548271 ID - pug01:8548271 LA - eng TI - Stein's method for comparison of univariate distributions PY - 2017 JO - (2017) PROBABILITY SURVEYS SN - 1549-5787 PB - 2017 AU - Ley, Christophe AU - Reinert, Gesine AU - Swan, Yvik AB - We propose a new general version of Stein's method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution which is based on a linear difference or differential-type operator. The resulting Stein identity highlights the unifying theme behind the literature on Stein's method (both for continuous and discrete distributions). Viewing the Stein operator as an operator acting on pairs of functions, we provide an extensive toolkit for distributional comparisons. Several abstract approximation theorems are provided. Our approach is illustrated for comparison of several pairs of distributions: normal vs normal, sums of independent Rademacher vs normal, normal vs Student, and maximum of random variables vs exponential, Frechet and Gumbel. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 8548271 | ||
005 | 20180409140721.0 | ||
008 | 180207s2017------------------------eng-- | ||
022 | a 1549-5787 | ||
024 | a 1854/LU-8548271 2 handle | ||
024 | a 10.1214/16-PS278 2 doi | ||
040 | a UGent | ||
245 | a Stein's method for comparison of univariate distributions | ||
260 | c 2017 | ||
520 | a We propose a new general version of Stein's method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution which is based on a linear difference or differential-type operator. The resulting Stein identity highlights the unifying theme behind the literature on Stein's method (both for continuous and discrete distributions). Viewing the Stein operator as an operator acting on pairs of functions, we provide an extensive toolkit for distributional comparisons. Several abstract approximation theorems are provided. Our approach is illustrated for comparison of several pairs of distributions: normal vs normal, sums of independent Rademacher vs normal, normal vs Student, and maximum of random variables vs exponential, Frechet and Gumbel. | ||
598 | a A2 | ||
100 | a Ley, Christophe u WE02 0 802002090889 | ||
700 | a Reinert, Gesine | ||
700 | a Swan, Yvik | ||
650 | a Mathematics and Statistics | ||
653 | a MULTIVARIATE NORMAL APPROXIMATION | ||
653 | a CENTRAL-LIMIT-THEOREM | ||
653 | a VARIANCE | ||
653 | a BOUNDS | ||
653 | a ORTHOGONAL POLYNOMIALS | ||
653 | a EXCHANGEABLE PAIRS | ||
653 | a EXPONENTIAL | ||
653 | a APPROXIMATION | ||
653 | a BINOMIAL APPROXIMATION | ||
653 | a RANDOM-VARIABLES | ||
653 | a INEQUALITIES | ||
653 | a CONVERGENCE | ||
653 | a Density approach | ||
653 | a Stein's method | ||
653 | a comparison of distributions | ||
773 | t PROBABILITY SURVEYS g Probab. Surv. 2017. 14 p.1-52 q 14:<1 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/8548271/file/8548273 z [open] y getdocbf05.pdf | ||
920 | a article | ||
852 | x WE b WE02 | ||
922 | a UGENT-WE |
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