A general moment bound for a product of Gaussian vector's functionals and a central limit theorem for subordinated Gaussian triangular arrays

Jean-Marc Bardet (1) , Donatas Surgailis (2, 3)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 Vilnius Institute of Mathematics and Informatics
3 Institute of Mathematics and Informatics

A general moment bound for a product of Gaussian vector's functions extending the moment bound in Taqqu (1977, Lemma 4.5) is established. A very general central limit theorem for triangular arrays of nonlinear functionals of multidimensional Gaussian sequences generalizing the results of Arcones (1994) is deduced. The stationarity of the Gaussian vector sequences is not required.

Mots clés: Central limit theorem for triangular arrays; Moment bound for Gaussian vector's functions; Hermitian decomposition; Diagram formula; Long memory processes.; Long memory processes

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-Marc Bardet, Donatas Surgailis. A general moment bound for a product of Gaussian vector's functionals and a central limit theorem for subordinated Gaussian triangular arrays. 2011. ⟨hal-00588606v1⟩