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二次谱估计量的偏误修正AI 解读

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…

Welch 谱密度估计方法的去偏AI 解读

Abstract Welch’s method provides an estimator of the power spectral density that is statistically consistent. This is achieved by averaging over periodograms calculated from overlapping segments of a time series. For a finite-length time series, while the variance of the estimator decreases as the number of segments increases, the magnitude of the estimator’s bias increases: a bias-variance trade-off ensues when setting the segment number. We address this issue by providing…

去偏 Whittle 似然AI 解读

The Whittle likelihood is a widely used and computationally efficient pseudolikelihood. However, it is known to produce biased parameter estimates with finite sample sizes for large classes of models. We propose a method for debiasing Whittle estimates for second-order stationary stochastic processes. The debiased Whittle likelihood can be computed in the same |${O}(n\log n)$| operations as the standard Whittle approach. We demonstrate the superior performance of our method…