# Adaptive Huber Regression on Markov-dependent Data

arXiv: https://arxiv.org/abs/1904.09027 · HTML: https://mlsanity.com/paper/1904.09027/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2019.

## Built on by (most cited first, 4 of 4)

- [Online Estimation and Inference for Robust Policy Evaluation in Reinforcement Learning](https://mlsanity.com/paper/2310.02581/) (2023)
- [Markov subsampling based Huber Criterion](https://mlsanity.com/paper/2112.06134/) (2021)
- [Covariate shift in nonparametric regression with Markovian design](https://mlsanity.com/paper/2307.08517/) (2023)
- [TailedTS: Benchmark Dataset for Heavy-Tailed Time Series Prediction and Periodicity Quantification](https://mlsanity.com/paper/2605.16361/) (2026)

## Abstract (arXiv)

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, Zhou, Fan, 2019, J. Amer. Stat. Assoc., in press] 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.