Limit theorems for Toeplitz quadratic functionals of continuous-time stationary processes

DOI10.1007/s00440-006-0037-yzbMath1113.60027OpenAlexW2132159708MaRDI QIDQ880943

Mamikon S. Ginovyan, Artur A. Sahakyan

Publication date: 21 May 2007

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-006-0037-y

zbMATH Keywords

Spectral densityToeplitz type quadratic functionalCentral limit theoremsStationary Gaussian process

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10)

Related Items

Statistical inference for stationary linear models with tapered data, Robust estimation for continuous-time linear models with memory, Unnamed Item, Estimation of spectral functionals for Lévy-driven continuous-time linear models with tapered data, Error bounds for approximations of traces of products of truncated Toeplitz operators, The trace problem for Toeplitz matrices and operators and its impact in probability, Functional limit theorems for Toeplitz quadratic functionals of continuous time Gaussian stationary processes, On the robustness to small trends of parameter estimation for continuous-time stationary models with memory, Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields, Parameter estimation for Lévy-driven continuous-time linear models with tapered data, Limit theorems for quadratic forms of Lévy-driven continuous-time linear processes, Limit theorems for tapered Toeplitz quadratic functionals of continuous-time Gaussian stationary processes, A note on approximations of traces of products of truncated Toeplitz matrices, On the trace approximation problem for truncated Toeplitz operators and matrices, 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 Toeplitz-type quadratic functionals of stationary processes and applications, Statistical estimation for stationary models with tapered data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A noncentral limit theorem for quadratic forms of Gaussian stationary sequences
• Convergence to a Gaussian limit as the normalization exponent tends to 1/2
• Berry-Esseen theorems for quadratic forms of Gaussian stationary processes
• Central limit theorems for quadratic forms in random variables having long-range dependence
• Asymptotically efficient nonparametric estimation of functionals of a spectral density function
• On bilinear forms in Gaussian random variables and Toeplitz matrices
• Convergence in distribution of sums of bivariate Appell polynomials with long-range dependence
• On Toeplitz type quadratic functionals of stationary Gaussian processes
• Large deviations for quadratic functionals of Gaussian processes
• Asymptotic theory of statistical inference for time series
• A note on central limit theorem for Toeplitz type quadratic forms in stationary Gaussian variables
• A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimate
• On Estimating the Value of a Linear Functional of the Spectral Density of a Gaussian Stationary Process
• On the Central Limit Theorem for Toeplitz Quadratic Forms of Stationary Sequences
• On Estimation of the Spectral Function of a Stationary Gaussian Process