Related papers: Cellwise and Casewise Robust Multivariate Regressi…
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…
Cellwise outliers are likely to occur together with casewise outliers in modern data sets with relatively large dimension. Recent work has shown that traditional robust regression methods may fail for data sets in this paradigm. The…
Multivariate location and scatter matrix estimation is a cornerstone in multivariate data analysis. We consider this problem when the data may contain independent cellwise and casewise outliers. Flat data sets with a large number of…
The cellwise robust M regression estimator is introduced as the first estimator of its kind that intrinsically yields both a map of cellwise outliers consistent with the linear model, and a vector of regression coefficients that is robust…
Large datasets are often affected by cell-wise outliers in the form of missing or erroneous data. However, discarding any samples containing outliers may result in a dataset that is too small to accurately estimate the covariance matrix.…
The usual Minimum Covariance Determinant (MCD) estimator of a covariance matrix is robust against casewise outliers. These are cases (that is, rows of the data matrix) that behave differently from the majority of cases, raising suspicion…
Regression is the workhorse of statistics, and is often faced with real data that contain outliers. When these are casewise outliers, that is, cases that are entirely wrong or belong to a different population, the issue can be remedied by…
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…
Classical discriminant analysis (DA) is based on the mean and empirical covariance matrix of each class, both of which are sensitive to outliers in the data. In the past the focus was on casewise outliers, that is, datapoints that lie far…
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 propose a data-analytic method for detecting cellwise outliers. Given a robust covariance matrix, outlying cells (entries) in a row are found by the cellHandler technique which combines lasso regression with a stepwise application of…
The Seemingly Unrelated Regressions (SUR) model is a wide used estimation procedure in econometrics, insurance and finance, where very often, the regression model contains more than one equation. Unknown parameters, regression coefficients…
In statistics and machine learning, the traditional meaning of the terms `outlier' and `anomaly' is a case in the dataset that behaves differently from the bulk of the data. This raises suspicion that it may belong to a different…
Tensor-on-tensor (TOT) regression is an important tool for the analysis of tensor data, aiming to predict a set of response tensors from a corresponding set of predictor tensors. However, standard TOT regression is sensitive to outliers,…
There is a great need for robust techniques in data mining and machine learning contexts where many standard techniques such as principal component analysis and linear discriminant analysis are inherently susceptible to outliers.…
Principal component analysis (PCA) is a fundamental tool for analyzing multivariate data. Here the focus is on dimension reduction to the principal subspace, characterized by its projection matrix. The classical principal subspace can be…
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…
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…
A robust estimation framework for binary regression models is studied, aiming to extend traditional approaches like logistic regression models. While previous studies largely focused on logistic models, we explore a broader class of models…
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…