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Related papers: Adaptive Huber Regression on Markov-dependent Data

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Stochastic approximation (SA) is a fundamental iterative framework with broad applications in reinforcement learning and optimization. Classical analyses typically rely on martingale difference or Markov noise with bounded second moments,…

Machine Learning · Computer Science 2026-03-23 Siddharth Chandak , Anuj Yadav , Ayfer Ozgur , Nicholas Bambos

Gaussian mixtures are commonly used for modeling heavy-tailed error distributions in robust linear regression. Combining the likelihood of a multivariate robust linear regression model with a standard improper prior distribution yields an…

Statistics Theory · Mathematics 2023-01-05 Haoxiang Li , Qian Qin , Galin L. Jones

Considered here are robust subgroup-classifier learning and testing in change-plane regressions with heavy-tailed errors, which can identify subgroups as a basis for making optimal recommendations for individualized treatment. A new…

Methodology · Statistics 2024-08-27 Xu Liu , Jian Huang , Yong Zhou , Xiao Zhang

In this paper, we develop a novel high-dimensional coefficient estimation procedure based on high-frequency data. Unlike usual high-dimensional regression procedures such as LASSO, we additionally handle the heavy-tailedness of…

Methodology · Statistics 2025-10-22 Minseok Shin , Donggyu Kim

This paper investigates the stability of deep ReLU neural networks for nonparametric regression under the assumption that the noise has only a finite p-th moment. We unveil how the optimal rate of convergence depends on p, the degree of…

Statistics Theory · Mathematics 2023-01-02 Jianqing Fan , Yihong Gu , Wen-Xin Zhou

Appropriate models for spatially autocorrelated data account for the fact that observations are not independent. A popular model in this context is the simultaneous autoregressive (SAR) model that allows to model the spatial dependency…

Methodology · Statistics 2017-07-12 A. Kreuzer , T. Erhardt , T. Nagler , C. Czado

In this paper we propose the Highly Adaptive Ridge (HAR): a regression method that achieves a $n^{-1/3}$ dimension-free L2 convergence rate in the class of right-continuous functions with square-integrable sectional derivatives. This is a…

Machine Learning · Statistics 2024-10-04 Alejandro Schuler , Alexander Hagemeister , Mark van der Laan

We consider strictly stationary heavy tailed time series whose finite-dimensional exponent measures are concentrated on axes, and hence their extremal properties cannot be tackled using classical multivariate regular variation that is…

Statistics Theory · Mathematics 2014-10-10 Rafal Kulik , Philippe Soulier

Estimating the transition dynamics of controlled Markov chains is crucial in fields such as time series analysis, reinforcement learning, and system exploration. Traditional non-parametric density estimation methods often assume independent…

Statistics Theory · Mathematics 2025-05-21 Imon Banerjee , Vinayak Rao , Harsha Honnappa

In this paper, we develop connections between two seemingly disparate, but central, models in robust statistics: Huber's epsilon-contamination model and the heavy-tailed noise model. We provide conditions under which this connection…

Machine Learning · Statistics 2019-07-03 Adarsh Prasad , Sivaraman Balakrishnan , Pradeep Ravikumar

Datasets with extreme observations and/or heavy-tailed error distributions are commonly encountered and should be analyzed with careful consideration of these features from a statistical perspective. Small deviations from an assumed model,…

Methodology · Statistics 2023-01-12 Meadhbh O'Neill , Kevin Burke

Human mobility prediction is crucial for applications ranging from location-based recommendations to urban planning, which aims to forecast users' next location visits based on historical trajectories. While existing mobility prediction…

Artificial Intelligence · Computer Science 2026-03-03 Yu Wang , Junshu Dai , Yuchen Ying , Hanyang Yuan , Zunlei Feng , Tongya Zheng , Mingli Song

Sparse linear regression methods generally have a free hyperparameter which controls the amount of sparsity, and is subject to a bias-variance tradeoff. This article considers the use of Aggregated hold-out to aggregate over values of this…

Statistics Theory · Mathematics 2022-12-08 Guillaume Maillard

The Huber's criterion is a useful method for robust regression. The adaptive least absolute shrinkage and selection operator (lasso) is a popular technique for simultaneous estimation and variable selection. In the case of small sample size…

Statistics Theory · Mathematics 2012-07-31 Laurent Zwald , Sophie Lambert-Lacroix

We investigate high-dimensional sparse regression when both the noise and the design matrix exhibit heavy-tailed behavior. Standard algorithms typically fail in this regime, as heavy-tailed covariates distort the empirical risk geometry. We…

Methodology · Statistics 2026-01-12 Kaiyuan Zhou , Xiaoyu Zhang , Wenyang Zhang , Di Wang

This paper introduces a robust and computationally efficient estimation framework for high-dimensional volatility models in the BEKK-ARCH class. The proposed approach employs data truncation to ensure robustness against heavy-tailed…

Statistics Theory · Mathematics 2026-05-26 Kejun Chen , Yuchang Lin , Qianqian Zhu

The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual…

Applications · Statistics 2014-07-08 Abhik Ghosh

Recently, high dimensional vector auto-regressive models (VAR), have attracted a lot of interest, due to novel applications in the health, engineering and social sciences. The presence of temporal dependence poses additional challenges to…

Statistics Theory · Mathematics 2022-09-20 Sagnik Halder , George Michailidis

The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…

Computation · Statistics 2019-05-08 Jim Griffin , Krys Latuszynski , Mark Steel

Reduced rank regression (RRR) is a fundamental tool for modeling multiple responses through low-dimensional latent structures, offering both interpretability and strong predictive performance in high-dimensional settings. Classical RRR…

Methodology · Statistics 2026-01-01 The Tien Mai