Moment bounds and central limit theorems for Gaussian subordinated 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 sums of products of Gaussian vector's functions extending the moment bound in Taqqu (1977, Lemma 4.5) is established. A general central limit theorem for triangular arrays of nonlinear functionals of multidimensional non-stationary Gaussian sequences is proved. This theorem extends the previous results of Breuer and Major (1981), Arcones (1994) and others. A Berry-Esseen-type bound in the above-mentioned central limit theorem is derived following Nourdin, Peccati and Podolskij (2011). Two applications of the above results are discussed. The first one refers to the asymptotic behavior of a roughness statistic for continuous-time Gaussian processes and the second one is a central limit theorem satisfied by long memory locally stationary process.

Mots clés: Central limit theorem for triangular arrays; Moment bound for Gaussian vector's functions; Hermitian decomposition; Diagram formula; Berry-Esseen bounds; Long memory processes; Locally stationary process.; Locally stationary process

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

Jean-Marc Bardet, Donatas Surgailis. Moment bounds and central limit theorems for Gaussian subordinated arrays. Journal of Multivariate Analysis, 2013, 114, pp.457-473. ⟨hal-00588606v2⟩