相关论文: Non-asymptotic robustness analysis of regression d…

Notions of depth in regression have been introduced and studied in the literature. Regression depth (RD) of Rousseeuw and Hubert (1999), the most famous one, is a direct extension of Tukey location depth (Tukey (1975)) to regression. Like…

The concept of statistical depth extends the notions of the median and quantiles to other statistical models. These procedures aim to formalize the idea of identifying deeply embedded fits to a model that are less influenced by…

Depth notions in regression have been systematically proposed and examined in Zuo (2018). One of the prominent advantages of notion of depth is that it can be directly utilized to introduce median-type deepest estimating functionals (or…

We study the behavior of high-dimensional robust regression estimators in the asymptotic regime where $p/n$ tends to a finite non-zero limit. More specifically, we study ridge-regularized estimators, i.e…

Regression neural networks (NNs) are most commonly trained by minimizing the mean squared prediction error, which is highly sensitive to outliers and data contamination. Existing robust training methods for regression NNs are often limited…

Robust estimation of a mean vector, a topic regarded as obsolete in the traditional robust statistics community, has recently surged in machine learning literature in the last decade. The latest focus is on the sub-Gaussian performance and…

Many modern datasets are collected automatically and are thus easily contaminated by outliers. This led to a regain of interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the…

Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to classical techniques based on maximum likelihood and related methods. Basu et al. (1998) introduced the density power divergence…

The Rousseeuw-Croux $S_n$, $Q_n$ scale estimators and the median absolute deviation $\operatorname{MAD}_n$ can be used as consistent estimators for the standard deviation under normality. All of them are highly robust: the breakdown point…

The minimum density power divergence estimator (MDPDE) has gained significant attention in the literature of robust inference due to its strong robustness properties and high asymptotic efficiency; it is relatively easy to compute and can…

Notion of median in one dimension is a foundational element in nonparametric statistics. It has been extended to multi-dimensional cases both in location and in regression via notions of data depth. Regression depth (RD) and projection…

Data on rates, percentages or proportions arise frequently in many different applied disciplines like medical biology, health care, psychology and several others. In this paper, we develop a robust inference procedure for the beta…

Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite-sample efficiency of…

This paper studies robust regression in the settings of Huber's $\epsilon$-contamination models. We consider estimators that are maximizers of multivariate regression depth functions. These estimators are shown to achieve minimax rates in…

Robust estimation under Huber's $\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Statistically optimal procedures such as Tukey's median and other estimators based on depth…

The problem of robust mean estimation in high dimensions is studied, in which a certain fraction (less than half) of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, the robust mean estimation problem is…

In this paper, we develop a robust non-parametric realized integrated beta estimator using high-frequency financial data contaminated by microstructure noises, which is robust to the stylized features, such as the time-varying beta and the…

Notions of depth in regression have been introduced and studied in the literature. The most famous example is Regression Depth (RD), which is a direct extension of location depth to regression. The projection regression depth (PRD) is the…

When the experimental data set is contaminated, we usually employ robust alternatives to common location and scale estimators such as the sample median and Hodges-Lehmann estimators for location and the sample median absolute deviation and…

Recent developments on deep learning established some theoretical properties of deep neural networks estimators. However, most of the existing works on this topic are restricted to bounded loss functions or (sub)-Gaussian or bounded input.…