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

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.

Published in at http://dx.doi.org/10.1214/12-AOP775 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Central limit theorems for sequences of multiple stochastic integrals
• Stein's method and exact Berry--Esseen asymptotics for functionals of Gaussian fields

Cited by in corpus (8)

• Sojourn measures of Student and Fisher-Snedecor random fields
• Limit theorems for weighted functionals of cyclical long-range dependent random fields
• On the rate of convergence to Rosenblatt-type distribution
• Functional Limit Theorems for Volterra Processes and Applications to Homogenization
• Humbert Generalized Fractional Differenced ARMA Processes
• Asymptotic Behaviour of Discretised Functionals of Long-Range Dependent Functional Data
• Convergence Rate Analysis in Limit Theorems for Nonlinear Functionals of the Second Wiener Chaos
• Multiscaling limit theorems for stochastic FPDE with cyclic long-range dependence