Adaptive Huber regression on Markov-dependent data

Jianqing Fan, Yongyi Guo, Bai Jiang

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


High-dimensional linear regression has been intensively studied in the community of statistics in the last two decades. For the convenience of theoretical analyses, classical methods usually assume independent observations and sub-Gaussian-tailed errors. However, neither of them hold in many real high-dimensional time-series data. Recently (Sun et al., 2019) proposed Adaptive Huber Regression (AHR) to address the issue of heavy-tailed errors. They discover that the robustification parameter of the Huber loss should adapt to the sample size, the dimensionality, and the moments of the heavy-tailed errors. We progress in a vertical direction and justify AHR on dependent observations. Specifically, we consider an important dependence structure — Markov dependence. Our results show that the Markov dependence impacts on the adaption of the robustification parameter and the estimation of regression coefficients in the way that the sample size should be discounted by a factor depending on the spectral gap of the underlying Markov chain.

Original languageEnglish (US)
Pages (from-to)802-818
Number of pages17
JournalStochastic Processes and their Applications
StatePublished - Aug 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Statistics and Probability
  • Modeling and Simulation


  • Adaptive Huber regression
  • Dependent observations
  • Heavy-tailed errors
  • High-dimensional regression
  • Markov chain


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