The Annals of Probability

Limit theorems for weighted nonlinear transformations of Gaussian stationary processes with singular spectra

Alexander V. Ivanov, Nikolai Leonenko, María D. Ruiz-Medina, and Irina N. Savich

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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.

Article information

Source
Ann. Probab., Volume 41, Number 2 (2013), 1088-1114.

Dates
First available in Project Euclid: 8 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aop/1362750952

Digital Object Identifier
doi:10.1214/12-AOP775

Mathematical Reviews number (MathSciNet)
MR3077537

Zentralblatt MATH identifier
1329.60031

Subjects
Primary: 62F05: Asymptotic properties of tests 60G10: Stationary processes 60G20: Generalized stochastic processes
Secondary: 60G15: Gaussian processes 62J02: General nonlinear regression

Keywords
Central limit theorem isonormal processes long-range dependence multiple singular spectra nonlinear transformations of random processes Wiener chaos

Citation

Ivanov, Alexander V.; Leonenko, Nikolai; Ruiz-Medina, María D.; Savich, Irina N. Limit theorems for weighted nonlinear transformations of Gaussian stationary processes with singular spectra. Ann. Probab. 41 (2013), no. 2, 1088--1114. doi:10.1214/12-AOP775. https://projecteuclid.org/euclid.aop/1362750952


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