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On Estimation of Convergence Rate of Statistics Expectancy LT to Linear Functional of Spectral Density L(f) of Stationary Gaussian Process

Authors: Shomakhov A.Yu. Published: 14.10.2013
Published in issue: #1(36)/2010  
DOI:

 
Category: Mathematics  
Keywords: stationary process, periodogram of a process, spectral density, spectral mean, asymptotic unbiasedness, Nikolsky classes, Feuer kernel

For the real-valued stationary Gaussian centered process X(t), having a spectral density f(λ), a problem is considered of estimating the convergence rate of expectancy of statistics LT = S ϕ(λ)IT(λ)dλ, where IT(λ) is a periodogram of a process X(t), to a linear functional of the spectral density L(f) = S ϕ(λ)f(λ)dλ of the stationary Gaussian process based on the sample {X(t), 0 ≤ t ≤ T}.