The optimal fourth moment theorem

Ivan Nourdin; Giovanni Peccati

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arXiv · 1305.1527

The optimal fourth moment theorem

Ivan Nourdin·Giovanni Peccati

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Abstract

We compute the exact rates of convergence in total variation associated with the 'fourth moment theorem' by Nualart and Peccati (2005), stating that a sequence of random variables living in a fixed Wiener chaos verifies a central limit theorem (CLT) if and only if the sequence of the corresponding fourth cumulants converges to zero. We also provide an explicit illustration based on the Breuer-Major CLT for Gaussian-subordinated random sequences.

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Ivan Nourdin, Giovanni Peccati. 2013-05-07. The optimal fourth moment theorem. https://arxiv.org/abs/1305.1527

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