In this article, we prove that in the Rademacher setting, a random vector with chaotic components is close in distribution to a centered Gaussian vector, if both the maximal influence of the associated kernel and the fourth cumulant of each component is small. In particular, we recover the univariate case recently established in Döbler and Krokowski (2019). Our main strategy consists in a novel adaption of the exchangeable pairs couplings initiated in Nourdin and Zheng (2017), as well as its combination with estimates via chaos decomposition.
Accepté le :
DOI : 10.1051/ps/2019013
Keywords: Fourth moment theorem, Rademacher chaos, Stein’s method, exchangeable pairs, spectral decomposition, maximal influence
Zheng, Guangqu 1
@article{PS_2019__23__874_0,
author = {Zheng, Guangqu},
title = {A {Peccati-Tudor} type theorem for {Rademacher} chaoses},
journal = {ESAIM: Probability and Statistics},
pages = {874--892},
year = {2019},
publisher = {EDP Sciences},
volume = {23},
doi = {10.1051/ps/2019013},
mrnumber = {4045540},
zbl = {1506.60036},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2019013/}
}
Zheng, Guangqu. A Peccati-Tudor type theorem for Rademacher chaoses. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 874-892. doi: 10.1051/ps/2019013
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