Related papers: Robust Estimation in Generalised Linear Models : T…
The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…
Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of $K$ Gaussians with generic means…
The assumption that response and predictor belong to the same statistical unit may be violated in practice. Unbiased estimation and recovery of true label ordering based on unlabeled data are challenging tasks and have attracted increasing…
D&R is a statistical approach designed to handle large and complex datasets. It partitions the dataset into several manageable subsets and subsequently applies the analytic method to each subset independently to obtain results. Finally, the…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
We propose a general approach to construct weighted likelihood estimating equations with the aim of obtain robust estimates. The weight, attached to each score contribution, is evaluated by comparing the statistical data depth at the model…
Generalized linear models are widely used in many areas of knowledge. As in other classes of regression models, it is desirable to perform diagnostic analysis in generalized linear models using residuals that are approximately standard…
Linear mixed models (LMMs) are used extensively to model dependecies of observations in linear regression and are used extensively in many application areas. Parameter estimation for LMMs can be computationally prohibitive on big data.…
In this paper we formulate a solution of the robust linear regression problem in a general framework of correntropy maximization. Our formulation yields a unified class of estimators which includes the Gaussian and Laplacian kernel-based…
When multiple models are considered in regression problems, the model averaging method can be used to weigh and integrate the models. In the present study, we examined how the goodness-of-prediction of the estimator depends on the…
Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has…
The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…
Multiple linear regression is a basic statistical tool, yielding a prediction formula with the input variables, slopes, and an intercept. But is it really easy to see which terms have the largest effect, or to explain why the prediction of…
Power and sample size calculations for Wald tests in generalized linear models (GLMs) are often limited to specific cases like logistic regression. More general methods typically require detailed study parameters that are difficult to…
Density modeling is notoriously difficult for high dimensional data. One approach to the problem is to search for a lower dimensional manifold which captures the main characteristics of the data. Recently, the Gaussian Process Latent…
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…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
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…
Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models…
Kernel Regularized Least Squares (KRLS) is a popular method for flexibly estimating models that may have complex relationships between variables. However, its usefulness to many researchers is limited for two reasons. First, existing…