Related papers: Robustifying multiple-set linear canonical analysi…

We introduce a class of regularized M-estimators of multivariate scatter and show, analogous to the popular spatial sign covariance matrix (SSCM), that they possess high breakdown points. We also show that the SSCM can be viewed as an…

To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods explicitly or implicitly depend on the kernel covariance operator (kernel CO) or kernel…

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…

Consider a logistic partially linear model, in which the logit of the mean of a binary response is related to a linear function of some covariates and a nonparametric function of other covariates. We derive simple, doubly robust estimators…

Under a partially linear models we study a family of robust estimates for the regression parameter and the regression function when some of the predictor variables take values on a Riemannian manifold. We obtain the consistency and the…

Parametric high-dimensional regression analysis requires the usage of regularization terms to get interpretable models. The respective estimators can be regarded as regularized M-functionals which are naturally highly nonlinear. We study…

We consider inference in linear regression models that is robust to heteroskedasticity and the presence of many control variables. When the number of control variables increases at the same rate as the sample size the usual…

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.,…

Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…

Many unsupervised kernel methods rely on the estimation of the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). Both kernel CO and kernel CCO are sensitive to contaminated data, even when bounded…

Partially linear additive models generalize linear ones since they model the relation between a response variable and covariates by assuming that some covariates have a linear relation with the response but each of the others enter through…

In this paper we propose an extension of the classical Sobol' estimator for the estimation of variance based sensitivity indices. The approach assumes a linear correlation model between the input variables which is used to decompose the…

Canonical correlation analysis is a family of multivariate statistical methods for the analysis of paired sets of variables. Since its proposition, canonical correlation analysis has for instance been extended to extract relations between…

There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two type of robust…

A wide array of graphical models can be parametrised to have atomic probabilities represented by monomial functions. Such monomial structure has proven very useful when studying robustness under the assumption of a multilinear model where…

We consider the scenario where one observes an outcome variable and sets of features from multiple assays, all measured on the same set of samples. One approach that has been proposed for dealing with this type of data is ``sparse multiple…

A robust and sparse estimator for multinomial regression is proposed for high dimensional data. Robustness of the estimator is achieved by trimming the observations, and sparsity of the estimator is obtained by the elastic net penalty,…

We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear…

This paper concerns robust inference on average treatment effects following model selection. In the selection on observables framework, we show how to construct confidence intervals based on a doubly-robust estimator that are robust to…

Canonical correlation analysis is a technique to extract common features from a pair of multivariate data. In complex situations, however, it does not extract useful features because of its linearity. On the other hand, kernel method used…