Debiasing Welch's method for spectral density estimation
成果类型：
Article
署名作者：
Astfalck, Lachlan C.; Sykulski, Adam M.; Cripps, Edward J.
署名单位：
University of Western Australia; Imperial College London
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asae033
发表日期：
2024
页码：
13131329
关键词：
摘要：
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 a novel method for debiasing Welch's method that maintains the computational complexity and asymptotic consistency, and leads to improved finite-sample performance. Theoretical results are given for fourth-order stationary processes with finite fourth-order moments and an absolutely convergent fourth-order cumulant function. The significant bias reduction is demonstrated with numerical simulation and an application to real-world data. Our estimator also permits irregular spacing over frequency and we demonstrate how this may be employed for signal compression and further variance reduction. The code accompanying this work is available in R and python.