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Density estimation and inference methods are widely used in empirical work. When the underlying distribution has compact support, conventional kernel-based density estimators are no longer consistent near or at the boundary because of their…

Computation · Statistics 2021-02-24 Matias D. Cattaneo , Michael Jansson , Xinwei Ma

As the most fundamental problem in statistics, robust location estimation has many prominent solutions, such as the trimmed mean, Winsorized mean, Hodges Lehmann estimator, Huber M estimator, and median of means. Recent studies suggest that…

Statistics Theory · Mathematics 2024-09-12 Li Tuobang

This paper considers the design of a minimax test for two hypotheses where the actual probability densities of the observations are located in neighborhoods obtained by placing a bound on the relative entropy between actual and nominal…

Information Theory · Computer Science 2016-11-18 Bernard C. Levy

This paper revisits the classical problem of interval estimation of a binomial proportion under Huber contamination. Our main result derives the rate of optimal interval length when the contamination proportion is unknown under a local…

Statistics Theory · Mathematics 2026-01-13 Minjun Cho , Yuetian Luo , Chao Gao

In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…

Methodology · Statistics 2018-07-13 Denis Belomestny , Alexander Goldenshluger

Most linear experimental design problems assume homogeneous variance although heteroskedastic noise is present in many realistic settings. Let a learner have access to a finite set of measurement vectors $\mathcal{X}\subset \mathbb{R}^d$…

Statistics Theory · Mathematics 2024-09-19 Justin Weltz , Tanner Fiez , Alexander Volfovsky , Eric Laber , Blake Mason , Houssam Nassif , Lalit Jain

Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is…

Machine Learning · Statistics 2017-01-17 Song Mei , Yu Bai , Andrea Montanari

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…

Methodology · Statistics 2015-02-05 L. A. Garcia-Escudero , A. Gordaliza , F. Greselin , S. Ingrassia , A. Mayo-Iscar

We tackle modelling and inference for variable selection in regression problems with many predictors and many responses. We focus on detecting hotspots, i.e., predictors associated with several responses. Such a task is critical in…

We study the problem of identifying change points in high-dimensional generalized linear models, and propose an approach based on sample-weighted empirical risk minimization. Our method, Weighted ERM, encodes priors on the change points via…

Methodology · Statistics 2026-04-14 Gabriel Arpino , Ramji Venkataramanan

We study nonparametric regression over Besov spaces from noisy observations under sub-exponential noise, aiming to achieve minimax-optimal guarantees on the integrated squared error that hold with high probability and adapt to the unknown…

Statistics Theory · Mathematics 2026-02-13 Paul Liautaud , Pierre Gaillard , Olivier Wintenberger

Despite tremendous advancements of machine learning models and algorithms in various application domains, they are known to be vulnerable to subtle, natural or intentionally crafted perturbations in future input data, known as adversarial…

Machine Learning · Statistics 2025-06-03 Jingfu Peng , Yuhong Yang

In small area estimation, it is a smart strategy to rely on data measured over time. However, linear mixed models struggle to properly capture time dependencies when the number of lags is large. Given the lack of published studies…

Gaussian mixture models are widely used to study clustering problems. These model-based clustering methods require an accurate estimation of the unknown data density by Gaussian mixtures. In Maugis and Michel (2009), a penalized maximum…

Statistics Theory · Mathematics 2015-03-19 Maugis Cathy , Michel Bertrand

Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the…

Methodology · Statistics 2023-04-10 Ayanendranath Basu , Abhik Ghosh , María Jaenada , Leandro Pardo

Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust…

Computation · Statistics 2017-10-02 Marina Valdora , Claudio Agostinelli , Victor J. Yohai

Within the framework of smoothing spline ANOVA, we propose a plug-in kernel ridge regression estimator to estimate the derivatives of the underlying multivariate regression function. We first establish an $L_\infty$ convergence rate of the…

Methodology · Statistics 2026-03-03 Ruiqi Liu , Kexuan Li , Meng Li

We show both adaptive and non-adaptive minimax rates of convergence for a family of weighted Laplacian-Eigenmap based nonparametric regression methods, when the true regression function belongs to a Sobolev space and the sampling density is…

Statistics Theory · Mathematics 2023-11-02 Zhaoyang Shi , Krishnakumar Balasubramanian , Wolfgang Polonik

We propose a test-time defense mechanism against adversarial attacks: imperceptible image perturbations that significantly alter the predictions of a model. Unlike existing methods that rely on feature filtering or smoothing, which can lead…

Computer Vision and Pattern Recognition · Computer Science 2025-10-06 Dong Lao , Yuxiang Zhang , Haniyeh Ehsani Oskouie , Yangchao Wu , Alex Wong , Stefano Soatto

We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings.…

Machine Learning · Statistics 2018-04-23 Adarsh Prasad , Arun Sai Suggala , Sivaraman Balakrishnan , Pradeep Ravikumar