English
Related papers

Related papers: A robust, adaptive M-estimator for pointwise estim…

200 papers

A new gradient-based adaptive sampling method is proposed for design of experiments applications which balances space filling, local refinement, and error minimization objectives while reducing reliance on delicate tuning parameters. High…

Methodology · Statistics 2024-05-09 Lucas Caparini , Gwynn J. Elfring , Mauricio Ponga

This paper presents a novel approach for pointwise estimation of multivariate density functions on known domains of arbitrary dimensions using nonparametric local polynomial estimators. Our method is highly flexible, as it applies to both…

Statistics Theory · Mathematics 2025-07-22 Karine Bertin , Nicolas Klutchnikoff , Frédéric Ouimet

This article is dedicated to the estimation of the regression function when the explanatory variable is a weakly dependent process whose correlation coefficient exhibits exponential decay and has a known bounded density function. The…

Statistics Theory · Mathematics 2025-07-17 Karine Bertin , Lisandro Fermin , Miguel Padrino

Heavy-tailed errors impair the accuracy of the least squares estimate, which can be spoiled by a single grossly outlying observation. As argued in the seminal work of Peter Huber in 1973 [{\it Ann. Statist.} {\bf 1} (1973) 799--821], robust…

Statistics Theory · Mathematics 2017-11-16 Wen-Xin Zhou , Koushiki Bose , Jianqing Fan , Han Liu

Sparse linear regression methods such as Lasso require a tuning parameter that depends on the noise variance, which is typically unknown and difficult to estimate in practice. In the presence of heavy-tailed noise or adversarial outliers,…

Statistics Theory · Mathematics 2025-06-17 Takeyuki Sasai , Hironori Fujisawa

We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model selection procedure is proposed. Under general moment conditions on the noise distribution a sharp…

Statistics Theory · Mathematics 2017-03-28 Vlad Barbu , Slim Beltaif , Serguei Pergamenchtchikov

This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…

Statistics Theory · Mathematics 2020-07-28 Jose Blanchet , Peter W. Glynn , Jun Yan , Zhengqing Zhou

For the sparse vector model, we consider estimation of the target vector, of its L2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with…

Statistics Theory · Mathematics 2020-03-04 Laëtitia Comminges , Olivier Collier , Mohamed Ndaoud , Alexandre B. Tsybakov

This paper concerns the estimation of the regression function at a given point in nonparametric heteroscedastic models with Gaussian noise or with noise having unknown distribution. In the two cases an asymptotically efficient kernel…

Statistics Theory · Mathematics 2007-11-30 Jean-Yves Brua

A scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of a…

Statistics Theory · Mathematics 2016-01-25 Tim Patschkowski , Angelika Rohde

We study confidence interval construction for linear regression under Huber's contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood,…

Statistics Theory · Mathematics 2026-04-03 Dong Xie , Chao Gao , John Lafferty

Convex and penalized robust regression methods often suffer from a persistent bias induced by large outliers, limiting their effectiveness in adversarial or heavy-tailed settings. In this work, we study a smooth redescending non-convex…

Statistics Theory · Mathematics 2025-12-01 Ilyes Hammouda , Mohamed Ndaoud , Abd-Krim Seghouane

A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly…

Statistics Theory · Mathematics 2021-02-08 Gaelle Chagny , Antoine Channarond , Van Ha Hoang , Angelina Roche

We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…

Machine Learning · Statistics 2015-03-19 Tianqi Zhao , Mladen Kolar , Han Liu

We study the adaptive minimax estimation of non-linear integral functionals of a density and extend the results obtained for linear and quadratic functionals to general functionals. The typical rate optimal non-adaptive minimax estimators…

Statistics Theory · Mathematics 2016-01-12 Rajarshi Mukherjee , Eric Tchetgen Tchetgen , James Robins

We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…

Statistics Theory · Mathematics 2024-07-16 Céline Duval , Émeline Schmisser

In this article we consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises observed in discrete time moments. An adaptive model selection procedure is proposed. A sharp…

Statistics Theory · Mathematics 2020-05-15 Vlad Stefan Barbu , Slim Beltaief , Serguei Pergamenshchikov

We consider the non-parametric regression problem under Huber's $\epsilon$-contamination model, in which an $\epsilon$ fraction of observations are subject to arbitrary adversarial noise. We first show that a simple local binning median…

Statistics Theory · Mathematics 2018-05-29 Simon S. Du , Yining Wang , Sivaraman Balakrishnan , Pradeep Ravikumar , Aarti Singh

This paper proposes a new method for estimating high-dimensional binary choice models. We consider a semiparametric model that places no distributional assumptions on the error term, allows for heteroskedastic errors, and permits endogenous…

Econometrics · Economics 2025-07-15 Fu Ouyang , Thomas Tao Yang

Asymmetry along with heteroscedasticity or contamination often occurs with the growth of data dimensionality. In ultra-high dimensional data analysis, such irregular settings are usually overlooked for both theoretical and computational…

Statistics Theory · Mathematics 2022-07-20 Bin Luo , Xiaoli Gao