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March 2013 Limit theorems for weighted nonlinear transformations of Gaussian stationary processes with singular spectra
Alexander V. Ivanov, Nikolai Leonenko, María D. Ruiz-Medina, Irina N. Savich
Ann. Probab. 41(2): 1088-1114 (March 2013). DOI: 10.1214/12-AOP775

Abstract

The limit Gaussian distribution of multivariate weighted functionals of nonlinear transformations of Gaussian stationary processes, having multiple singular spectra, is derived, under very general conditions on the weight function. This paper is motivated by its potential applications in nonlinear regression, and asymptotic inference on nonlinear functionals of Gaussian stationary processes with singular spectra.

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Alexander V. Ivanov. Nikolai Leonenko. María D. Ruiz-Medina. Irina N. Savich. "Limit theorems for weighted nonlinear transformations of Gaussian stationary processes with singular spectra." Ann. Probab. 41 (2) 1088 - 1114, March 2013. https://doi.org/10.1214/12-AOP775

Information

Published: March 2013
First available in Project Euclid: 8 March 2013

zbMATH: 1329.60031
MathSciNet: MR3077537
Digital Object Identifier: 10.1214/12-AOP775

Subjects:
Primary: 60G10 , 60G20 , 62F05
Secondary: 60G15 , 62J02

Keywords: central limit theorem , isonormal processes , long-range dependence , multiple singular spectra , nonlinear transformations of random processes , Wiener Chaos

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 2 • March 2013
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