On Asymptotic Unbiasedness of the Estimator for the Linear Functional of Spectral Density of Stationary Gaussian Process

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Abstract


For the real-valued stationary Gaussian centered process X(t), t ? R, R = (- ?; + ? ), having a spectral density f(?), a problem of asymptotic unbiasedness is considered for the estimator (statistics) LT = ? ?(?)IT(?)d?, ? ?(- ?; + ? ), where is IT(?) a periodogram of a process, for the linear functional of the spectral density L(f) = ? ?(?)f(?)d? of the stationary Gaussian centered process based on the sample {X (t),0 ? t ? T }.

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A Yu Shomakhov

Plekhanov Russian University of Economics

Plekhanov Russian University of Economics

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Copyright (c) 2011 Шомахов А.Ю.

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