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arXiv: 1104.4732

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Journal of Multivariate Analysis 114 (2013) 457-473

Available versions:

v1 (2011-04-25)

v2 (2012-08-08)

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

Subject

:

Mathematics/Statistics Statistics/Statistics Theory

Keyword(s): 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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From: Jean-Marc Bardet <>

Submitted on: Tuesday, 7 August 2012 08:02:53

Updated on: Thursday, 28 February 2013 21:41:26