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A large dimensional characterization of robust M-estimators of covariance (or scatter) is provided under the assumption that the dataset comprises independent (essentially Gaussian) legitimate samples as well as arbitrary deterministic…
We study robust regression under a contamination model in which covariates are clean while the responses may be corrupted in an adaptive manner. Unlike the classical Huber's contamination model, where both covariates and responses may be…
Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the…
In many applications, when building linear regression models, it is important to account for the presence of outliers, i.e., corrupted input data points. Such problems can be formulated as mixed-integer optimization problems involving cubic…
We analyze the statistical consistency of robust estimators for precision matrices in high dimensions. We focus on a contamination mechanism acting cellwise on the data matrix. The estimators we analyze are formed by plugging appropriately…
Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently…
Principal Component Analysis (PCA) finds a linear mapping and maximizes the variance of the data which makes PCA sensitive to outliers and may cause wrong eigendirection. In this paper, we propose techniques to solve this problem; we use…
Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…
We consider robust location-scale estimators under contamination. We show that commonly used robust estimators such as the median and the Huber estimator are inconsistent under asymmetric contamination, while the Tukey estimator is…
Covariance matrix estimation is one of the most important problems in statistics. To accommodate the complexity of modern datasets, it is desired to have estimation procedures that not only can incorporate the structural assumptions of…
Gaussian process regression (GPR) model is well-known to be susceptible to outliers. Robust process regression models based on t-process or other heavy-tailed processes have been developed to address the problem. However, due to the nature…
Bai (2010) and Bai et al. (2012) proposed robust mixture regression method based on the M regression estimation. However, the M-estimators are robust against the outliers in response variables, but they are not robust against the outliers…
Today's data pose unprecedented challenges to statisticians. It may be incomplete, corrupted or exposed to some unknown source of contamination. We need new methods and theories to grapple with these challenges. Robust estimation is one of…
When applying a statistical method in practice it often occurs that some observations deviate from the usual assumptions. However, many classical methods are sensitive to outliers. The goal of robust statistics is to develop methods that…
In statistical inference, we commonly assume that samples are independent and identically distributed from a probability distribution included in a pre-specified statistical model. However, such an assumption is often violated in practice.…
Robust estimators of large covariance matrices are considered, comprising regularized (linear shrinkage) modifications of Maronna's classical M-estimators. These estimators provide robustness to outliers, while simultaneously being…
In an industrial context, the activity of sensors is recorded at a high frequency. A challenge is to automatically detect abnormal measurement behavior. Considering the sensor measures as functional data, the problem can be formulated as…
A robust estimator for a wide family of mixtures of linear regression is presented. Robustness is based on the joint adoption of the Cluster Weighted Model and of an estimator based on trimming and restrictions. The selected model provides…
Cellwise outliers are widespread in data and traditional robust methods may fail when applied to datasets under such contamination. We propose a variable selection procedure, that uses a pairwise robust estimator to obtain an initial…
Algorithmic robust statistics has traditionally focused on the contamination model where a small fraction of the samples are arbitrarily corrupted. We consider a recent contamination model that combines two kinds of corruptions: (i) small…