Moment bounds and central limit theorems for Gaussian subordinated arrays
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 (1983) , Arcones (1994)  and others. A Berry–Esseen-type bound in the above-mentioned central limit theorem is derived following Nourdin et al. (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 processes.
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Volume (Year): 114 (2013)
Issue (Month): C ()
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- Nourdin, Ivan & Peccati, Giovanni & Podolskij, Mark, 2011.
"Quantitative Breuer-Major theorems,"
Stochastic Processes and their Applications,
Elsevier, vol. 121(4), pages 793-812, April.
- Ivan Nourdin & Giovanni Peccati & Mark Podolskij, 2010. "Quantitative Breuer-Major Theorems," CREATES Research Papers 2010-22, Department of Economics and Business Economics, Aarhus University.
- Soulier, Philippe, 2001. "Moment bounds and central limit theorem for functions of Gaussian vectors," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 193-203, September.
- Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
- Coulon-Prieur, Clémentine & Doukhan, Paul, 2000. "A triangular central limit theorem under a new weak dependence condition," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 61-68, March. Full references (including those not matched with items on IDEAS)
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