The optimal fourth moment theorem

By Ivan Nourdin, Giovanni Peccati. 2013

92 citations recorded by the source corpus.

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.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6c2ead430192479f00542080b684bfd82aca9e06

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Citations in the corpus

Optimal rates for parameter estimation of stationary Gaussian processes (2016, methodology): “– Therefore we choose to consider polynomial variations of these processes, which then necessarily live in Wiener chaos, whose properties are now well understood thanks to new Malliavin-calculus advances which were initiated by Nourdin and Peccati in 2008; in particular, we rely a general observatio”
The Variance-Gamma Distribution: A Review (2023, unknown): “For f ∈ H 2, we denote the double Wiener-Itô integral by I2(f) (see Nourdin and Peccati [88, Section 2.7] for a definition and fundamental properties).”
Malliavin-Stein method for variance-gamma approximation on Wiener space (2014, background): “However, our rate is still not optimal as shown by the main result in [15].”