Related papers: Adaptive Huber Regression on Markov-dependent Data

As one of the triumphs and milestones of robust statistics, Huber regression plays an important role in robust inference and estimation. It has also been finding a great variety of applications in machine learning. In a parametric setup, it…

We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error…

Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. To investigate their asymptotic behaviors, they require a sub-Gaussian or finite high-order…

Huber regression (HR) is a popular robust alternative to the least squares regression when the error follows a heavy-tailed distribution. We propose a new method called the enveloped Huber regression (EHR) by considering the envelope…

We study in this paper the problem of least absolute deviation (LAD) regression for high-dimensional heavy-tailed time series which have finite $\alpha$-th moment with $\alpha \in (1,2]$. To handle the heavy-tailed dependent data, we…

We study the problem of modelling high-dimensional, heavy-tailed time series data via a factor-adjusted vector autoregressive (VAR) model, which simultaneously accounts for pervasive co-movements of the variables by a handful of factors, as…

We investigate the high-dimensional properties of robust regression estimators in the presence of heavy-tailed contamination of both the covariates and response functions. In particular, we provide a sharp asymptotic characterisation of…

High dimensional Vector Autoregressions (VAR) have received a lot of interest recently due to novel applications in health, engineering, finance and the social sciences. Three issues arise when analyzing VAR's: (a) The high dimensional…

Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…

We propose a multivariate generative model to capture the complex dependence structure often encountered in business and financial data. Our model features heterogeneous and asymmetric tail dependence between all pairs of individual…

We study the stochastic linear bandits with heavy-tailed noise. Two principled strategies for handling heavy-tailed noise, truncation and median-of-means, have been introduced to heavy-tailed bandits. Nonetheless, these methods rely on…

In this paper, we propose self-tuned robust estimators for estimating the mean of heavy-tailed distributions, which refer to distributions with only finite variances. Our approach introduces a new loss function that considers both the mean…

For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…

We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…

Longitudinal data often involve heterogeneity, sparse signals, and contamination from response outliers or high-leverage observations especially in biomedical science. Existing methods usually address only part of this problem, either…

In this work, we develop a constructive modeling framework for extreme threshold exceedances in repeated observations of spatial fields, based on general product mixtures of random fields possessing light or heavy-tailed margins and various…

Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…

Our goal is to develop a Bayesian model averaging technique in linear regression models that accommodates heavier tailed error densities than the normal distribution. Motivated by the use of the Huber loss function in the presence of…

The autoregressive (AR) model is a widely used model to understand time series data. Traditionally, the innovation noise of the AR is modeled as Gaussian. However, many time series applications, for example, financial time series data, are…