Related papers: Uniform bounds for robust mean estimators

We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains the…

We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…

We develop a procedure that transforms any asymptotically normal estimator into an asymptotically normal estimator whose distribution is robust to arbitrary data contamination. More generally, our procedure transforms any estimator whose…

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…

The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…

In this paper, we develop efficient randomized algorithms for estimating probabilistic robustness margin and constructing robustness degradation curve for uncertain dynamic systems. One remarkable feature of these algorithms is their…

This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions;…

The concept of statistical depth extends the notions of the median and quantiles to other statistical models. These procedures aim to formalize the idea of identifying deeply embedded fits to a model that are less influenced by…

Many works in statistics aim at designing a universal estimation procedure, that is, an estimator that would converge to the best approximation of the (unknown) data generating distribution in a model, without any assumption on this…

In this paper, we consider the situation in which the observations follow an isotonic generalized partly linear model. Under this model, the mean of the responses is modelled, through a link function, linearly on some covariates and…

Real data are rarely pure. Hence the past half-century has seen great interest in robust estimation algorithms that perform well even when part of the data is corrupt. However, their vast majority approach optimal accuracy only when given a…

We present \textit{universal} estimators for the statistical mean, variance, and scale (in particular, the interquartile range) under pure differential privacy. These estimators are universal in the sense that they work on an arbitrary,…

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.,…

The goal of this note is to present a modification of the popular median of means estimator that achieves sub-Gaussian deviation bounds with nearly optimal constants under minimal assumptions on the underlying distribution. We build on a…

A robust mean value is often a good alternative to the standard mean value when dealing with data containing many outliers. An efficient method for samples of one-dimensional features and the truncated quadratic error norm is presented and…

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

The problem of robust mean estimation in high dimensions is studied, in which a certain fraction (less than half) of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, the robust mean estimation problem is…

This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the…

The paper proposes some robust estimators of the finite population mean. Such estimators are particularly suitable in the presence of some outlying observations. Included as special cases of our general result are robust versions of the…

We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…