A Peccati-Tudor type theorem for Rademacher chaoses
ESAIM: Probability and Statistics, Tome 23 (2019), pp. 874-892.

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.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2019013
Classification : 60F05, 60B12, 47N30
Mots-clés : Fourth moment theorem, Rademacher chaos, Stein’s method, exchangeable pairs, spectral decomposition, maximal influence
Zheng, Guangqu 1

1
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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. http://archive.numdam.org/articles/10.1051/ps/2019013/

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