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 \(\Phi (\hat \theta _T ),{\text{ where }}\hat \theta _T \) is a suitable sequence of T 1/2-consistent estimators of unknown spectral density θ(λ), is H 0- and IK-asymptotically efficient estimator for a nonlinear smooth functional Φ(θ).
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Ginovian, M.S. Asymptotically Efficient Nonparametric Estimation of Nonlinear Spectral Functionals. Acta Applicandae Mathematicae 78, 145–154 (2003). https://doi.org/10.1023/A:1025708727313
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DOI: https://doi.org/10.1023/A:1025708727313