Bias correction of quadratic spectral estimators
Lachlan Astfalck, Adam M. Sykulski, Edward Jerrold Cripps · Biometrika · 2025
Summary The three cardinal, statistically consistent families of nonparametric estimators for the power spectral density of a time series are the lag-window, multitaper and Welch estimators. However, when estimating power spectral densities from a finite sample, each can be subject to nonignorable bias. Astfalck et al. (2024) 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 providing 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 the $ {O}(n\log n) $ which is typical in spectral analyses, but it is not insurmountable in practice. Simulation studies support the theory with comparisons across variations of quadratic estimators.