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Estimation of spectral functionals for Lévy-driven continuous-time linear models with tapered data. (English) Zbl 1462.62228

Summary: The paper is concerned with the nonparametric statistical estimation of linear spectral functionals for Lévy-driven continuous-time stationary linear models with tapered data. As an estimator for unknown functional we consider the averaged tapered periodogram. We analyze the bias of the estimator and obtain sufficient conditions assuring the proper rate of convergence of the bias to zero, necessary for asymptotic normality of the estimator. We prove a a central limit theorem for a suitable normalized stochastic process generated by a tapered Toeplitz type quadratic functional of the model. As a consequence of these results we obtain the asymptotic normality of our estimator.

MSC:

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62M15 Inference from stochastic processes and spectral analysis
60G10 Stationary stochastic processes
60F05 Central limit and other weak theorems
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