Related papers: Cellwise Robust M Regression
To perform multiple regression, the least squares estimator is commonly used. However, this estimator is not robust to outliers. Therefore, robust methods such as S-estimation have been proposed. These estimators flag any observation with a…
The inflated beta regression model is widely used for modeling continuous proportions with values at the boundaries. Maximum likelihood estimation for these models is well-known for its sensitivity to outliers, which can severely distort…
Linear mixed models (LMMs) are a popular class of methods for analyzing longitudinal and clustered data. However, such models can be sensitive to outliers, and this can lead to biased inference on model parameters and inaccurate prediction…
We investigate two important properties of M-estimator, namely, robustness and tractability, in linear regression setting, when the observations are contaminated by some arbitrary outliers. Specifically, robustness means the statistical…
Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…
Machine learning and data analysis have been used in many robotics fields, especially for modelling. Data are usually the result of sensor measurements and, as such, they might be subjected to noise and outliers. The presence of outliers…
A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough…
Cellwise Robust Twoblock (CRTB) is introduced, the first cellwise robust method for simultaneous dimension reduction of multivariate predictor and response blocks, in both a dense and a sparse variable-selecting variant. Classical robust…
This paper concerns the robust regression model when the number of predictors and the number of observations grow in a similar rate. Theory for M-estimators in this regime has been recently developed by several authors [El Karoui et al.,…
Principal component regression uses principal components as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We…
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…
Whole robustness is a nice property to have for statistical models. It implies that the impact of outliers gradually vanishes as they approach plus or minus infinity. So far, the Bayesian literature provides results that ensure whole…
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…
Additive regression models have a long history in multivariate nonparametric regression. They provide a model in which each regression function depends only on a single explanatory variable allowing to obtain estimators at the optimal…
This paper proposes an original approach to better understanding the behavior of robust scatter matrix $M$-estimators. Scatter matrices are of particular interest for many signal processing applications since the resulting performance…
This paper studies robust regression for data on Riemannian manifolds. Geodesic regression is the generalization of linear regression to a setting with a manifold-valued dependent variable and one or more real-valued independent variables.…
Quantile Regression (QR) can be used to estimate aleatoric uncertainty in deep neural networks and can generate prediction intervals. Quantifying uncertainty is particularly important in critical applications such as clinical diagnosis,…
We propose a class of robust estimates for multivariate linear models. Based on the approach of MM estimation (Yohai 1987), we estimate the regression coefficients and the covariance matrix of the errors simultaneously. These estimates have…
Parameter estimation of mixture regression model using the expectation maximization (EM) algorithm is highly sensitive to outliers. Here we propose a fast and efficient robust mixture regression algorithm, called Component-wise Adaptive…
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…