The three cardinal, statistically consistent, families of nonparametric estimators to the power spectral density of a time series are lag-window, multitaper and Welch estimators. However, when estimating power spectral densities from a finite sample each can be subject to nonignorable bias. astfalck2024debiasing developed a method that offers significant bias reduction for finite samples for Welch’s estimator, which this article extends to the larger family of quadratic estimators, thus offering similar theory for bias correction of lag-window and multitaper estimators as well as combinations thereof. Importantly, this theory may be used in conjunction with any and all tapers and lag-sequences designed for bias reduction, and so should be seen as an extension to valuable work in these fields, rather than a supplanting methodology. The order of computation is larger than O (n log n) which is typical in spectral analyses, but not insurmountable in practice. Simulation studies support the theory with comparisons across variations of quadratic estimators.
AbstractThe three cardinal, statistically consistent, families of nonparametric estimators to the power spectral density of a time series are lag-window, multitaper and Welch estimators. However, when estimating power spectral densities from a finite sample each can be subject to nonignorable bias. astfalck2024debiasing developed a method that offers significant bias reduction for finite samples for Welch’s estimator, which this article extends to the larger family of quadratic estimators, thus offering similar theory for bias correction of lag-window and multitaper estimators as well as combinations thereof. Importantly, this theory may be used in conjunction with any and all tapers and lag-sequences designed for bias reduction, and so should be seen as an extension to valuable work in these fields, rather than a supplanting methodology. The order of computation is larger than O (n log n) which is typical in spectral analyses, but not insurmountable in practice. Simulation studies support the theory with comparisons across variations of quadratic estimators. Read More
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