Non-Asymptotic Pointwise and Worst-Case Bounds for Classical Spectrum Estimators

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.