Moment bounds and central limit theorems for Gaussian subordinated arrays

JOURNAL OF MULTIVARIATE ANALYSIS

卷:114

Article

Bardet, Jean-Marc¹  Surgailis, Donatas² 

[1] Univ Paris 01, SAMM, F-75013 Paris, France

[2] Vilnius Univ, Inst Math & Informat, LT-08663 Vilnius, Lithuania

关键词: 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;   

DOI  :  10.1016/j.jmva.2012.08.002

来源: Elsevier

【 摘 要 】

A general moment bound for sums of products of Gaussian vector's functions extending the moment bound in Taqqu (1977, Lemma 4.5) [28] 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 (1983) [5], Arcones (1994) [1] and others. A Berry-Esseen-type bound in the above-mentioned central limit theorem is derived following Nourdin et al. (2011) [20]. 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 processes. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free