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

For the real-valued stationary Gaussian centered process X(t),t = 0,±1,±2…, with a spectral density f(λ), a problem is considered of estimating the convergence rate of expectancy of statistics LN = ∫ φ(λ)IN(λ)dλ,λ ∈ [−π;π], where IN(λ) is a periodogram of a process X(t), t = 0,±1,±2…, to a linear functional of the spectral density L(f) = ∫ φ(λ)f(λ)dλ of the stationary Gaussian process based on the sample {X(1), X(2),…,X(N)}.

stationary process, periodogram of a process, spectral density, spectral mean, asymptotic unbiasedness, Nikolsky classes, Fej´er kernel