Moment bounds and central limit theorems for Gaussian subordinated arrays
Abstract
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.
Keywords
Cite
@article{arxiv.1104.4732,
title = {Moment bounds and central limit theorems for Gaussian subordinated arrays},
author = {Jean-Marc Bardet and Donatas Surgailis},
journal= {arXiv preprint arXiv:1104.4732},
year = {2012}
}