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Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…
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…
The sample covariance matrix is a cornerstone of multivariate statistics, but it is highly sensitive to outliers. These can be casewise outliers, such as cases belonging to a different population, or cellwise outliers, which are deviating…
Linear regression with normally distributed errors - including particular cases such as ANOVA, Student's t-test or location-scale inference - is a widely used statistical procedure. In this case the ordinary least squares estimator…
We consider the problem of robust and adaptive model predictive control (MPC) of a linear system, with unknown parameters that are learned along the way (adaptive), in a critical setting where failures must be prevented (robust). This…
We study robust linear regression in high-dimension, when both the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\alpha=n/d$, and study a data model that includes outliers. We provide exact asymptotics for the…
The association between a continuous and an ordinal variable is commonly modeled through the polyserial correlation model. However, this model, which is based on a partially-latent normality assumption, may be misspecified in practice, due…
We study the problem of estimating the means of well-separated mixtures when an adversary may add arbitrary outliers. While strong guarantees are available when the outlier fraction is significantly smaller than the minimum mixing weight,…
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…
To date most linear and nonlinear Kalman filters (KFs) have been developed under the Gaussian assumption and the well-known minimum mean square error (MMSE) criterion. In order to improve the robustness with respect to impulsive (or…
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…
We revisit the problem of estimating the mean of a high-dimensional distribution in the presence of an $\varepsilon$-fraction of adversarial outliers. When $\varepsilon$ is at most some sufficiently small constant, previous works can…
Most of the regularization methods such as the LASSO have one (or more) regularization parameter(s), and to select the value of the regularization parameter is essentially equal to select a model. Thus, to obtain a model suitable for 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 consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the number of features p are both increasing such that $p/n \to…
Model mismatch and process noise are two frequently occurring phenomena that can drastically affect the performance of model predictive control (MPC) in practical applications. We propose a principled way to tune the cost function and the…
Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust…
Outlier detection algorithms typically assign an outlier score to each observation in a dataset, indicating the degree to which an observation is an outlier. However, these scores are often not comparable across algorithms and can be…
Polychoric correlation is often an important building block in the analysis of rating data, particularly for structural equation models. However, the commonly employed maximum likelihood (ML) estimator is highly susceptible to…
We present a framework to design nonlinear robust output feedback model predictive control (MPC) schemes that ensure constraint satisfaction under noisy output measurements and disturbances. We provide novel estimation methods to bound the…