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.

翻译：谱估计是时间序列数据分析中的基本方法，其应用领域涵盖医学、语音分析与控制设计。谱估计的渐近理论已得到充分研究，但当样本数量固定且有限时，该理论存在局限性。本文针对一类广泛的谱估计器，在特定频率的逐点意义下以及所有频率的最坏情形下，给出了非渐近误差界。该方法被用于推导经典Blackman-Tukey、Bartlett和Welch估计器的误差界。特别地，这些是Bartlett和Welch估计器的首批非渐近误差界。