mlsanityData to 14 Oct 2026

Concentration inequalities for high-dimensional linear processes with dependent innovations

arXiv 2307.12395 ↗First posted 23 Jul 2023math.ST stat.ME stat.MLcited by 1

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Abstract (arXiv)

We develop concentration inequalities for the l_∞ norm of vector linear processes with sub-Weibull, mixingale innovations. This inequality is used to obtain a concentration bound for the maximum entrywise norm of the lag-h autocovariance matrix of linear processes. We apply these inequalities to sparse estimation of large-dimensional VAR(p) systems and heterocedasticity and autocorrelation consistent (HAC) high-dimensional covariance estimation.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 15 of its 59 references that are in the map. First posted on arXiv 23 Jul 2023.

Builds on

15 of 59 references.

References · 15

  1. 2020Machine Learning Advances for Time Series Forecastingcited by 49
  2. 2018Moving Beyond Sub-Gaussianity in High-Dimensional Statistics: Applications in Covariance Estimation and Linear Regressioncited by 42
  3. 2013Regularized estimation in sparse high-dimensional time series modelscited by 41
  4. 2020Concentration Inequalities for Statistical Inferencecited by 24
  5. 2013Oracle Inequalities for High Dimensional Vector Autoregressionscited by 11
  6. 2021Sharper Sub-Weibull Concentrationscited by 8
  7. 2021Bridging factor and sparse modelscited by 6
  8. 2013A Direct Estimation of High Dimensional Stationary Vector Autoregressionscited by 5
  9. 2019Regularized Estimation of High-Dimensional Vector AutoRegressions with Weakly Dependent Innovationscited by 5
  10. 2021Rate-Optimal Robust Estimation of High-Dimensional Vector Autoregressive Modelscited by 4
  11. 2017Sparse Identification and Estimation of Large-Scale Vector AutoRegressive Moving Averagescited by 2
  12. 2018Bootstrap Based Inference for Sparse High-Dimensional Time Series Modelscited by 1
3 more
  1. 2021A Survey of Estimation Methods for Sparse High-dimensional Time Series Modelscited by 1
  2. 2021Sparse Generalized Yule-Walker Estimation for Large Spatio-temporal Autoregressions with an Application to NO2 Satellite Datacited by 1
  3. 2023Sparse High-Dimensional Vector Autoregressive Bootstrapcited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Tail-Aware Information-Theoretic Bounds for LLM Alignment under Heavy-Tailed Rewardscited by 0