Related papers: Robust Statistical Estimators with Bounded Empiric…

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…

This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a…

This paper is devoted to the estimators of the mean that provide strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. The main ideas behind proposed techniques are based on bridging the notions of…

We present new M-estimators of the mean and variance of real valued random variables, based on PAC-Bayes bounds. We analyze the non-asymptotic minimax properties of the deviations of those estimators for sample distributions having either a…

Let $X^{(n)}$ be an observation sampled from a distribution $P_{\theta}^{(n)}$ with an unknown parameter $\theta,$ $\theta$ being a vector in a Banach space $E$ (most often, a high-dimensional space of dimension $d$). We study the problem…

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…

We study the out-of-sample properties of robust empirical optimization problems with smooth $\phi$-divergence penalties and smooth concave objective functions, and develop a theory for data-driven calibration of the non-negative "robustness…

This paper considers an empirical likelihood inference for parameters defined by general estimating equations, when data are missing at random. The efficiency of existing estimators depends critically on correctly specifying the conditional…

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…

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…

Robust mean estimation is the problem of estimating the mean $\mu \in \mathbb{R}^d$ of a $d$-dimensional distribution $D$ from a list of independent samples, an $\epsilon$-fraction of which have been arbitrarily corrupted by a malicious…

In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, which ultimately…

This article studies the \emph{robust covariance matrix estimation} of a data collection $X = (x_1,\ldots,x_n)$ with $x_i = \sqrt \tau_i z_i + m$, where $z_i \in \mathbb R^p$ is a \textit{concentrated vector} (e.g., an elliptical random…

We prove a new bound on the average sensitivity of polynomial threshold functions. In particular we show that a polynomial threshold function of degree $d$ in at most $n$ variables has average sensitivity at most…

Assume that $X_{1}, \ldots, X_{N}$ is an $\varepsilon$-contaminated sample of $N$ independent Gaussian vectors in $\mathbb{R}^d$ with mean $\mu$ and covariance $\Sigma$. In the strong $\varepsilon$-contamination model we assume that the…

Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…

We study estimation of a multivariate function $f:\mathbf{R}^d\to\mathbf{R}$ when the observations are available from the function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are…

Estimating the effect of treatments from natural experiments, where treatments are pre-assigned, is an important and well-studied problem. We introduce a novel natural experiment dataset obtained from an early childhood literacy nonprofit.…

Estimating the mean of a random vector from i.i.d. data has received considerable attention, and the optimal accuracy one may achieve with a given confidence is fairly well understood by now. When the data take values in more general metric…

We propose an estimator for the mean of random variables in separable real Banach spaces using the empirical characteristic function. Assuming that the covariance operator of the random variable is bounded in a precise sense, we show that…