On Toeplitz type quadratic functionals of stationary Gaussian processes
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Publication:1343609
DOI10.1007/BF01193706zbMath0817.60018MaRDI QIDQ1343609
Publication date: 27 July 1995
Published in: Probability Theory and Related Fields (Search for Journal in Brave)
Gaussian processes (60G15) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Inference from stochastic processes and spectral analysis (62M15)
Related Items (28)
Quadratic-exponential functionals of Gaussian quantum processes ⋮ Statistical inference for stationary linear models with tapered data ⋮ Limit theorems for Toeplitz quadratic functionals of continuous-time stationary processes ⋮ State-space computation of quadratic-exponential functional rates for linear quantum stochastic systems ⋮ Efficient estimation of spectral functionals for continuous-time stationary models ⋮ 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 ⋮ Limit theorems for additive functionals of stationary fields, under integrability assumptions on the higher order spectral densities ⋮ Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields ⋮ Weak convergence of functionals of stationary long memory processes to Rosenblatt-type distributions ⋮ On the Whittle estimators for some classes of continuous-parameter random processes and fields ⋮ A sufficient condition for asymptotic normality of the normalized quadratic form \(\Psi_{n}(f,g)\) ⋮ Parameter estimation for Lévy-driven continuous-time linear models with tapered data ⋮ Goodness-of-fit tests for continuous-time stationary processes ⋮ 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 ⋮ Goodness-of-fit tests for stationary Gaussian processes with tapered data ⋮ 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 ⋮ A functional large deviations principle for quadratic forms of Gaussian stationary processes ⋮ Statistical estimation for stationary models with tapered data
Cites Work
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- 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
- A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimate
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