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arXiv · 1304.1934

Stein's method and a quantitative Lindeberg CLT for the Fourier transforms of random vectors

Ben Berckmoes·Bob Lowen·Jan Van Casteren
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Abstract

We use a multivariate version of Stein's method to establish a quantitative Lindeberg CLT for the Fourier transforms of random $N$-vectors. We achieve this by deducing a specific integral representation for the Hessian matrix of a solution to the Stein equation with test function $e_t(x) = \exp(- i \sum_{k=1}^N t_k x_k)$, where $t,x \in \mathbb{R}^N$.

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Ben Berckmoes, Bob Lowen, Jan Van Casteren. 2013-04-06. Stein's method and a quantitative Lindeberg CLT for the Fourier transforms of random vectors. https://arxiv.org/abs/1304.1934

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