Efficient Nonparametric Spectral Density Estimation with Randomly Censored Time Series

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2021-07-22

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Abstract

Spectral Density estimation is a well known problem for a directly observed time series. However, the literature on spectral density estimation for a randomly censored time series is next to none. The dissertation develops a sharp lower bound for the minimax mean integrated squared error (MISE) for an estimator of a spectral density for a zero-mean stationary time series. Then an efficient and data-driven spectral density estimator (E-estimator) is suggested, which adapts to unknown smoothness of the spectral density and distribution of a censored random variable. Asymptotic upper bound of the MISE of the proposed estimator is obtained and it attains the sharp lower bound, so the proposed estimator is sharp minimax (or efficient). The E-estimator is studied and compared with an Oracle and a Naive estimator via simulated and real examples. The studies exhibit this E-estimator performs well under various scenarios and can compete with the Oracle estimator in simulated and real examples.

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Spectral energy distribution, Time-series analysis, Chebyshev approximation, Analysis of covariance

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