Optimal Gamma Approximation on Wiener Space
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 -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 D\"obler 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.
Cite
@article{arxiv.1902.02658,
title = {Optimal Gamma Approximation on Wiener Space},
author = {Ehsan Azmoodeh and Peter Eichelsbacher and Lukas Knichel},
journal= {arXiv preprint arXiv:1902.02658},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1806.03878