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arXiv : 1104.4732

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Journal of Multivariate Analysis 114 (2013) 457-473

Versions disponibles :

v1 (25-04-2011)

v2 (08-08-2012)

Moment bounds and central limit theorems for Gaussian subordinated arrays

Jean-Marc Bardet 1, Donatas Surgailis 2, 3

(2013)

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.

1 :	Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM)
	Université Paris I - Panthéon-Sorbonne
2 :	Vilnius Institute of Mathematics and Informatics
	Vilnius University
3 :	Institute of Mathematics and Informatics
	Université de Vilnius

Domaine

:

Mathématiques/Statistiques Statistiques/Théorie

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.

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Contributeur : Jean-Marc Bardet <>

Soumis le : Mardi 7 Août 2012, 08:02:53

Dernière modification le : Jeudi 28 Février 2013, 21:41:26