Related papers: Least trimmed squares regression with missing valu…

This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and…

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…

The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…

We present a robust framework to perform linear regression with missing entries in the features. By considering an elliptical data distribution, and specifically a multivariate normal model, we are able to conditionally formulate a…

It has previously been shown that ordinary least squares can be used to estimate the coefficients of the single-index model under only mild conditions. However, the estimator is non-robust leading to poor estimates for some models. In this…

Inference in the presence of outliers is an important field of research as outliers are ubiquitous and may arise across a variety of problems and domains. Bayesian optimization is method that heavily relies on probabilistic inference. This…

This paper considers the problem of inference in a linear regression model with outliers where the number of outliers can grow with sample size but their proportion goes to 0. We apply the square-root lasso estimator penalizing the l1-norm…

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…

In regression analysis of multivariate data, it is tacitly assumed that response and predictor variables in each observed response-predictor pair correspond to the same entity or unit. In this paper, we consider the situation of "permuted…

Challenges with data in the big-data era include (i) the dimension $p$ is often larger than the sample size $n$ (ii) outliers or contaminated points are frequently hidden and more difficult to detect. Challenge (i) renders most conventional…

Health data are often not symmetric to be adequately modeled through the usual normal distributions; most of them exhibit skewed patterns. They can indeed be modeled better through the larger family of skew-normal distributions covering…

The task of robust linear estimation in the presence of outliers is of particular importance in signal processing, statistics and machine learning. Although the problem has been stated a few decades ago and solved using classical…

This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…

We adapt a manifold sampling algorithm for the nonsmooth, nonconvex formulations of learning that arise when imposing robustness to outliers present in the training data. We demonstrate the approach on objectives based on trimmed loss.…

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…

This paper proposes a framework for simultaneous dimensionality reduction and regression in the presence of outliers in data by applying low-rank and sparse matrix decomposition. For multivariate data corrupted with outliers, it is…

Outlier detection is an inevitable step to most statistical data analyses. However, the mere detection of an outlying case does not always answer all scientific questions associated with that data point. Outlier detection techniques,…

Outlying observations can be challenging to handle and adversely affect subsequent analyses, especially in data with increasing dimensional complexity. Although outliers are not always undesired anomalies in the data and may possess…

In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…

Model averaging is an alternative to model selection for dealing with model uncertainty, which is widely used and very valuable. However, most of the existing model averaging methods are proposed based on the least squares loss function,…