mlsanityData to 7 Oct 2026

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

arXiv 2303.11908 ↗First posted 21 Mar 2023math.ST cs.LG eess.SPcited by 4

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Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 10 of its 27 references that are in the map. First posted on arXiv 21 Mar 2023.

Builds on

10 of 27 references.

References · 10

  1. 2018Near optimal finite time identification of arbitrary linear dynamical systemscited by 89
  2. 2016Gradient Descent Learns Linear Dynamical Systemscited by 78
  3. 2018Non-asymptotic Identification of LTI Systems from a Single Trajectorycited by 77
  4. 2019Finite Sample Analysis of Stochastic System Identificationcited by 67
  5. 2019Non-asymptotic Closed-Loop System Identification using Autoregressive Processes and Hankel Model Reductioncited by 9
  6. 2018Spectral Analysis of High-dimensional Time Seriescited by 8
  7. 2022Frequency Domain Statistical Inference for High-Dimensional Time Seriescited by 6
  8. 2019Topology Learning of Linear Dynamical Systems with Latent Nodes using Matrix Decompositioncited by 4
  9. 2021Efficient and passive learning of networked dynamical systems driven by non-white exogenous inputscited by 4
  10. 2022Statistical inference for high-dimensional spectral density matrixcited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 0; 2026: 1.

4 papers.

  1. 2024Approximation with Random Shallow ReLU Networks with Applications to Model Reference Adaptive Controlcited by 4
  2. 2024Multi-Source and Test-Time Domain Adaptation on Multivariate Signals using Spatio-Temporal Monge Alignmentcited by 4
  3. 2023Information Theoretically Optimal Sample Complexity of Learning Dynamical Directed Acyclic Graphscited by 1
  4. 2026Simultaneous Pointwise Majorization for Mixed Tail Processes with Applications in Gaussian Chaos and Ergodic Diffusionscited by 0