2023/03/21 by Andrew Lamperski, Lamperski, Andrew · 2 citations
Mathematics · #Applied mathematics #Asymptotic analysis #Class (philosophy) #Computer science #Estimator #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (cs.LG) #Mathematical Approximation and Integration #Mathematical analysis #Mathematics #Pointwise #Series (stratigraphy) #Signal Processing (eess.SP) #Spectral density #Spectrum (functional analysis) #Statistical Methods and Inference #Statistics #Statistics Theory (math.ST) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2303.11908
openalex publication_date 2023/03/21 · openalex created_date 2023/03/23 · openalex updated_date 2026/07/28
Spectrum estimation is a fundamental methodology in the analysis of time-series data, with applications including medicine, speech analysis, and control design. The asymptotic theory of spectrum estimation is well-understood, but the theory is limited when the number of samples is fixed and finite. This paper gives non-asymptotic error bounds for a broad class of spectral estimators, both pointwise (at specific frequencies) and in the worst case over all frequencies. The general method is used to derive error bounds for the classical Blackman-Tukey, Bartlett, and Welch estimators. In particular, these are first non-asymptotic error bounds for Bartlett and Welch estimators.