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

DOI10.1214/12-AOP775zbMath1329.60031arXiv1303.4588MaRDI QIDQ1951702

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

Publication date: 24 May 2013

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.4588

zbMATH Keywords

central limit theoremlong-range dependenceWiener chaosnonlinear transformations of random processesisonormal processesmultiple singular spectra

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Inference from stochastic processes and spectral analysis (62M15) General nonlinear regression (62J02) Generalized stochastic processes (60G20)

Related Items (23)

Asymptotic normality of simultaneous estimators of cyclic long-memory processes ⋮ Functional limit theorems for Volterra processes and applications to homogenization* ⋮ On asymptotics of discretized functionals of long-range dependent functional data ⋮ Limit theorems for filtered long-range dependent random fields ⋮ Limit Theorems for Excursion Sets of Stationary Random Fields ⋮ Sojourn measures of Student and Fisher-Snedecor random fields ⋮ Central and Noncentral Limit Theorems Arising from the Scattering Transform and Its Neural Activation Generalization ⋮ Asymptotic properties of $M$-estimators of parameters of a nonlinear regression model with a random noise whose spectrum is singular ⋮ Asymptotic properties of Ibragimov’s estimator for a parameter of the spectral density of the random noise in a nonlinear regression model ⋮ Humbert generalized fractional differenced ARMA processes ⋮ On a class of minimum contrast estimators for Gegenbauer random fields ⋮ The asymptotic normality for the least squares estimator of parameters in a two dimensional sinusoidal model of observations ⋮ Non-central limit theorems and convergence rates ⋮ Some probability inequalities of least-squares estimator in non linear regression model with strong mixing errors ⋮ Large deviation for a least squares estimator in a nonlinear regression model ⋮ Asymptotic properties of the \(M\)-estimates of parameters in a nonlinear regression model with discrete time and singular spectrum ⋮ On the rate of convergence to Rosenblatt-type distribution ⋮ Limit Theorems for Weighted Functionals of Cyclical Long-Range Dependent Random Fields ⋮ Limit theorems for additive functionals of stationary fields, under integrability assumptions on the higher order spectral densities ⋮ Asymptotic expansion of the moments of correlogram estimator for the random-noise covariance function in the nonlinear regression model ⋮ Asymptotic properties of periodogram estimators in the trigonometric model for observations on the plane ⋮ On LSE in regression model for long-range dependent random fields on spheres ⋮ On the least squares estimator asymptotic normality of the multivariate symmetric textured surface parameters

Cites Work

• Asymptotic properties of the LSE in a regression model with long-memory stationary errors
• Wiener chaos: Moments, cumulants and diagrams. A survey with computer implementation
• Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields
• Multivariate normal approximation using Stein's method and Malliavin calculus
• Central limit theorems for non-linear functionals of Gaussian fields
• On estimation of a regression model with long-memory stationary errors
• A central limit theorem for the renormalized self-intersection local time of a stationary vector Gaussian process
• Necessary conditions for nonlinear functionals of Gaussian processes to satisfy central limit theorems
• Limit theorems for functionals of moving averages
• Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors
• Semiparametric analysis of long-range dependence in nonlinear regression
• Central limit theorems for sequences of multiple stochastic integrals
• On a Szegö type limit theorem, the Hölder-Young-Brascamp-Lieb inequality, and the asymptotic theory of integrals and quadratic forms of stationary fields
• Limit theorems for Fourier transforms of functionals of Gaussian sequences
• Weak convergence to fractional brownian motion and to the rosenblatt process
• Convergence of integrated processes of arbitrary Hermite rank
• Non-central limit theorems for non-linear functional of Gaussian fields
• Gaussian Hilbert Spaces
• Long memory with seasonal effects
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Limit theorems for weighted nonlinear transformations of Gaussian stationary processes with singular spectra