Related papers: Trimmed sample means for robust uniform mean estim…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
We consider estimation of the extreme value index and extreme quantiles for heavy-tailed data that are right-censored. We study a general procedure of removing low importance observations in tail estimators. This trimming procedure is…
In this paper, we develop connections between two seemingly disparate, but central, models in robust statistics: Huber's epsilon-contamination model and the heavy-tailed noise model. We provide conditions under which this connection…
In the setting of entangled single-sample distributions, the goal is to estimate some common parameter shared by a family of distributions, given one \emph{single} sample from each distribution. We study mean estimation and linear…
Let $X$ be a random variable with unknown mean and finite variance. We present a new estimator of the mean of $X$ that is robust with respect to the possible presence of outliers in the sample, provides tight sub-Gaussian deviation…
In this paper, we propose self-tuned robust estimators for estimating the mean of heavy-tailed distributions, which refer to distributions with only finite variances. Our approach introduces a new loss function that considers both the mean…
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…
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…
We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…
In recent years, partially observable functional data has gained significant attention in practical applications and has become the focus of increasing interest in the literature. In this thesis, we build upon the concept of data…
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…
We study the problem of learning generalized linear models under adversarial corruptions. We analyze a classical heuristic called the iterative trimmed maximum likelihood estimator which is known to be effective against label corruptions in…
A popular method for variance reduction in observational causal inference is propensity-based trimming, the practice of removing units with extreme propensities from the sample. This practice has theoretical grounding when the data are…
We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic…
Causal inference with observational studies often relies on the assumptions of unconfoundedness and overlap of covariate distributions in different treatment groups. The overlap assumption is violated when some units have propensity scores…
The last decade has seen a number of advances in computationally efficient algorithms for statistical methods subject to robustness constraints. An estimator may be robust in a number of different ways: to contamination of the dataset, to…
Adaptive experiment designs can dramatically improve statistical efficiency in randomized trials, but they also complicate statistical inference. For example, it is now well known that the sample mean is biased in adaptive trials.…
Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence…
This article proposes a new method of truncated estimation to estimate the tail index $\alpha$ of the extremely heavy-tailed distribution with infinite mean or variance. We not only present two truncated estimators $\hat{\alpha}$ and…
In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…