Quantitative Breuer-Major theorems
AbstractWe consider sequences of random variables of the type , n>=1, where is a d-dimensional Gaussian process and is a measurable function. It is known that, under certain conditions on f and the covariance function r of X, Sn converges in distribution to a normal variable S. In the present paper we derive several explicit upper bounds for quantities of the type , where h is a sufficiently smooth test function. Our methods are based on Malliavin calculus, on interpolation techniques and on the Stein's method for normal approximation. The bounds deduced in our paper depend only on and on simple infinite series involving the components of r. In particular, our results generalize and refine some classic CLTs given by Breuer and Major, Giraitis and Surgailis, and Arcones, concerning the normal approximation of partial sums associated with Gaussian-subordinated time series.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 121 (2011)
Issue (Month): 4 (April)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
Other versions of this item:
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
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- Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2009. "Multipower Variation for Brownian Semistationary Processes," CREATES Research Papers 2009-21, School of Economics and Management, University of Aarhus.
- Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij & Jeannette H.C. Woerner, 2008.
"Bipower variation for Gaussian processes with stationary increments,"
CREATES Research Papers
2008-21, School of Economics and Management, University of Aarhus.
- Barndorff-Nielsen, Ole E. & Corcuera, José Manuel & Podolskij, Mark, 2009. "Power variation for Gaussian processes with stationary increments," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1845-1865, June.
- Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2007. "Power variation for Gaussian processes with stationary increments," CREATES Research Papers 2007-42, School of Economics and Management, University of Aarhus.
- Corinne Berzin & José León, 2007. "Estimating the Hurst Parameter," Statistical Inference for Stochastic Processes, Springer, vol. 10(1), pages 49-73, 01.
- 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.
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