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• W2913056934 abstract "In cite{n-p-noncentral}, Nourdin and Peccati established a neat characterization of Gamma approximation on a fixed Wiener chaos in terms of convergence of only the third and fourth cumulants. In this paper, we provide an optimal rate of convergence in the $d_2$-distance in terms of the maximum of the third and fourth cumulants analogous to the result for normal approximation in cite{n-p-optimal}. In order to achieve our goal, we introduce a novel operator theory approach to Stein's method. The recent development in Stein's method for the Gamma distribution of Dobler and Peccati (cite{d-p}) plays a pivotal role in our analysis. Several examples in the context of quadratic forms are considered to illustrate our optimal bound." @default.
• W2913056934 created "2019-02-21" @default.
• W2913056934 creator A5011867447 @default.
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• W2913056934 date "2019-02-06" @default.
• W2913056934 modified "2023-09-27" @default.
• W2913056934 title "Optimal Gamma Approximation on Wiener Space" @default.
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• W2913056934 hasPublicationYear "2019" @default.
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