Related papers: Optimal Mean Estimation without a Variance
Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…
We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a non-asymptotic point of view. In particular, we define estimators with a…
A random variable $\xi$ has a {\it light-tailed} distribution (for short: is light-tailed) if it possesses a finite exponential moment, $\E \exp (\lambda \xi) <\infty$ for some $\lambda >0$, and has a {\it heavy-tailed} distribution (is…
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…
We revisit the problem of mean estimation in the Gaussian sequence model with $\ell_p$ constraints for $p \in [0, \infty]$. We demonstrate two phenomena for the behavior of the maximum likelihood estimator (MLE), which depend on the noise…
We consider a linear regression model with regression parameter beta=(beta_1,...,beta_p) and independent and identically N(0,sigma^2) distributed errors. Suppose that the parameter of interest is theta = a^T beta where a is a specified…
Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this…
We study the robust mean estimation problem in high dimensions, where $\alpha <0.5$ fraction of the data points can be arbitrarily corrupted. Motivated by compressive sensing, we formulate the robust mean estimation problem as the…
We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test…
This paper studies the distributed optimization problem under the influence of heavy-tailed gradient noises. Here, a heavy-tailed noise means that the noise does not necessarily satisfy the bounded variance assumption. Instead, it satisfies…
In this paper we estimate the mean-variance portfolio in the high-dimensional case using the recent results from the theory of random matrices. We construct a linear shrinkage estimator which is distribution-free and is optimal in the sense…
We study large deviation upper bounds and mean-squared error (MSE) guarantees of a general framework of nonlinear stochastic gradient methods in the online setting, in the presence of heavy-tailed noise. Unlike existing works that rely on…
Consider the problem of finding a population or a probability distribution amongst many with the largest mean when these means are unknown but population samples can be simulated or otherwise generated. Typically, by selecting largest…
Frequentist model averaging has been proposed as a method for incorporating "model uncertainty" into confidence interval construction. Such proposals have been of particular interest in the environmental and ecological statistics…
Historically, to bound the mean for small sample sizes, practitioners have had to choose between using methods with unrealistic assumptions about the unknown distribution (e.g., Gaussianity) and methods like Hoeffding's inequality that use…
We study the problem of high-dimensional robust mean estimation in an online setting. Specifically, we consider a scenario where $n$ sensors are measuring some common, ongoing phenomenon. At each time step $t=1,2,\ldots,T$, the $i^{th}$…
Construction of tight confidence regions and intervals is central to statistical inference and decision making. This paper develops new theory showing minimum average volume confidence regions for categorical data. More precisely, consider…
We obtain the upper error bounds of robust estimators for mean vector, using the median-of-means (MOM) method. The method is designed to handle data with heavy tails and contamination, with only a finite second moment, which is weaker than…
The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…
The Negative Binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard Normal approximation often does not provide adequate…