Berry-Esseen theorems for quadratic forms of Gaussian stationary processes

DOI10.1007/BF00699102zbMath0572.60030OpenAlexW2092846806MaRDI QIDQ1062347

Masanobu Taniguchi

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/bf00699102

zbMATH Keywords

spectral densityGaussian stationary processBerry-Esseen type theorem

Mathematics Subject Classification ID

Gaussian processes (60G15) Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Characteristic functions; other transforms (60E10)

Related Items (5)

On bilinear forms in Gaussian random variables and Toeplitz matrices ⋮ Limit theorems for Toeplitz quadratic functionals of continuous-time stationary processes ⋮ The trace problem for Toeplitz matrices and operators and its impact in probability ⋮ Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields ⋮ On Berry-Esseen bounds for non-instantaneous filters of linear processes

Cites Work

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• A Berry-Esseen theorem for linear combinations of order statistics
• Berry-Esseen theorems for simple linear rank statistics under the null- hypothesis
• \(L_1\) bounds for asymptotic normality of m-dependent sums using Stein's technique
• On the second order asymptotic efficiency of estimators of Gaussian ARMA processes
• THE APPROXIMATE DISTRIBUTION OF SERIAL CORRELATION COEFFICIENTS
• Approximations for densities of sufficient estimators
• The approximate distribution of partial serial correlation coefficients calculated from residuals from regression on Fourier series
• Asymptotic expansions for sums of weakly dependent random vectors

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