Related papers: M-Estimation Method Based Asymmetric Objective Fun…
Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite-sample efficiency of…
In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed, where the defining convex function has an exponential nature. These estimators avoid the necessity of using an intermediate kernel…
This paper proposes an adaptive penalized weighted mean regression for outlier detection of high-dimensional data. In comparison to existing approaches based on the mean shift model, the proposed estimators demonstrate robustness against…
We study weighted M-estimators for $\mathbb{R}^d$-valued clustered data and give sufficient conditions for their consistency. Their asymptotic normality is established with estimation of the asymptotic covariance matrix. We address the…
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…
A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each…
Suppose that we wish to estimate a finite-dimensional summary of one or more function-valued features of an underlying data-generating mechanism under a nonparametric model. One approach to estimation is by plugging in flexible estimates of…
Irregular functional data in which densely sampled curves are observed over different ranges pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in…
A new type of redescending M-estimators is constructed, based on data augmentation with an unspecified outlier model. Necessary and sufficient conditions for the convergence of the resulting estimators to the Hubertype skipped mean are…
We introduce a robust and fully adaptive method for pointwise estimation in heteroscedastic regression. We allow for noise and design distributions that are unknown and fulfill very weak assumptions only. In particular, we do not impose…
Multivariate sign functions are often used for robust estimation and inference. We propose using data dependent weights in association with such functions. The proposed weighted sign functions retain desirable robustness properties, while…
We observe a large number of functions differing from each other only by a translation parameter. While the main pattern is unknown, we propose to estimate the shift parameters using $M$-estimators. Fourier transform enables to transform…
A popular regularized (shrinkage) covariance estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward its grand mean. In this paper, a more general…
This paper deals with robust marginal estimation under a general regression model when missing data occur in the response and also in some of covariates. The target is a marginal location parameter which is given through an $M-$functional.…
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 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…
In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. At the…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
We study asymptotic behavior of one-step $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent $M$-estimators. These…
In this work, we propose an adaptive robust loss function framework for MHE, integrating an adaptive robust loss function to reduce the impact of outliers with a regularization term that avoids naive solutions. The proposed approach…