Asymptotically Efficient Nonparametric Estimation of Nonlinear Spectral Functionals |
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Authors: | M S Ginovian |
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Institution: | (1) Armenian National Academy of Sciences, Institute of Mathematics, Marshal Bagramian 24-B, Yerevan, Armenia |
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Abstract: | The paper considers a problem of construction of asymptotically efficient estimators for functionals defined on a class of spectral densities. We define the concepts of H
0- and IK-efficiency of estimators, based on the variants of Hájek–Ibragimov–Khas'minskii convolution theorem and Hájek–Le Cam local asymptotic minimax theorem, respectively. We prove that
is a suitable sequence of T
1/2-consistent estimators of unknown spectral density ( ), is H
0- and IK-asymptotically efficient estimator for a nonlinear smooth functional ( ). |
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Keywords: | stationary Gaussian process efficient estimation spectral density nonlinear spectral functionals periodogram local asymptotic normality |
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