Asymptotically efficient nonparametric estimation of functionals of a spectral density function

DOI10.1007/BF00776242zbMath0595.62037OpenAlexW1997247322MaRDI QIDQ1077836

I. A. Ibragimov, Rafail Z. Khasminskii

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1007/bf00776242

zbMATH Keywords

lower boundsspectral densityfunctionalsstationary Gaussian time seriesprecision of nonparametric estimators

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05)

Related Items (18)

Efficient estimation of functionals of the spectral density of stationary Gaussian fields ⋮ On some problems of nonparametric estimation ⋮ On Toeplitz type quadratic functionals of stationary Gaussian processes ⋮ Statistical inference for stationary linear models with tapered data ⋮ Limit theorems for Toeplitz quadratic functionals of continuous-time stationary processes ⋮ Efficient estimation of spectral functionals for continuous-time stationary models ⋮ Robust estimation for continuous-time linear models with memory ⋮ 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 ⋮ On estimating linear functional of the covariance function of a stationary process ⋮ 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 ⋮ Local asymptotic normality for autoregression with infinite order ⋮ A nonparametric estimator of a nonlinear functional of regression under a given plan ⋮ Asymptotically optimal estimation in misspecified time series models ⋮ Limit theorems for Toeplitz-type quadratic functionals of stationary processes and applications ⋮ Statistical estimation for stationary models with tapered data

Cites Work

• On a Non-Parametric Analogue of the Information Matrix
• Asymptotic inference in stationary Gaussian time-series
• On Estimation of the Spectral Function of a Stationary Gaussian Process
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