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High-dimensional data can often display heterogeneity due to heteroscedastic variance or inhomogeneous covariate effects. Penalized quantile and expectile regression methods offer useful tools to detect heteroscedasticity in…

$\ell_1$-penalized quantile regression is widely used for analyzing high-dimensional data with heterogeneity. It is now recognized that the $\ell_1$-penalty introduces non-negligible estimation bias, while a proper use of concave…

High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square…

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…

As an effective nonparametric method, empirical likelihood (EL) is appealing in combining estimating equations flexibly and adaptively for incorporating data information. To select important variables and estimating equations in the sparse…

Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…

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…

We investigate robust nonparametric regression in the presence of heavy-tailed noise, where the hypothesis class may contain unbounded functions and robustness is ensured via a robust loss function $\ell_\sigma$. Using Huber regression as a…

A current strand of research in high-dimensional statistics deals with robustifying the available methodology with respect to deviations from the pervasive light-tail assumptions. In this paper we consider a linear mean regression model…

This paper studies the non-asymptotic merits of the double $\ell_1$-regularized for heterogeneous overdispersed count data via negative binomial regressions. Under the restricted eigenvalue conditions, we prove the oracle inequalities for…

Recently, high-dimensional heterogeneous data have attracted a lot of attention and discussion. Under heterogeneity, semiparametric regression is a popular choice to model data in statistics. In this paper, we take advantages of expectile…

The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…

The ordinary least squares estimate in linear regression is sensitive to the influence of errors with large variance, which reduces its robustness, especially when dealing with heavy-tailed errors or outliers frequently encountered in…

High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…

We tackle estimating sparse coefficients in a linear regression when the covariates are sampled from an $L$-subexponential random vector. This vector belongs to a class of distributions that exhibit heavier tails than Gaussian random…

We consider both $\ell _{0}$-penalized and $\ell _{0}$-constrained quantile regression estimators. For the $\ell _{0}$-penalized estimator, we derive an exponential inequality on the tail probability of excess quantile prediction risk and…

Heavy-tailed error distributions and predictors with anomalous values are ubiquitous in high-dimensional regression problems and can seriously jeopardize the validity of statistical analyses if not properly addressed. For more reliable…

Heavy-tailed metrics are common and often critical to product evaluation in the online world. While we may have samples large enough for Central Limit Theorem to kick in, experimentation is challenging due to the wide confidence interval of…

We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…

We propose a doubly robust estimator for the average treatment effect in high dimensional low sample size observational studies, where contamination and model misspecification pose serious inferential challenges. The estimator combines…