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Title: Efficient nonparametric estimation of Toeplitz covariance matrices Authors:  Tatyana Krivobokova - University of Vienna (Austria) [presenting]
Abstract: A new nonparametric estimator for Toeplitz covariance matrices based on a periodic smoothing spline estimator of the log-spectral density function is proposed. This estimator is positive definite by construction, fully data-driven and computationally very fast. Moreover, the estimator is shown to be minimax optimal under the spectral norm for a large class of Toeplitz matrices. These results are readily extended to inverses of Toeplitz covariance matrices. Also, an alternative version of the Whittle likelihood for the spectral density based on the Discrete Cosine Transform (DCT) is proposed.