Related papers: Do we need to estimate the variance in robust mean…

Extremile (Daouia, Gijbels and Stupfler,2019) is a novel and coherent measure of risk, determined by weighted expectations rather than tail probabilities. It finds application in risk management, and, in contrast to quantiles, it fulfills…

Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…

Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues…

This paper introduces a new version of the smoothly trimmed mean with a more general version of weights, which can be used as an alternative to the classical trimmed mean. We derive its asymptotic variance and to further investigate its…

In existing distributed stochastic optimization studies, it is usually assumed that the gradient noise has a bounded variance. However, recent research shows that the heavy-tailed noise, which allows an unbounded variance, is closer to…

We study tail risk dynamics in high-frequency financial markets and their connection with trading activity and market uncertainty. We introduce a dynamic extreme value regression model accommodating both stationary and local unit-root…

In this paper, we study robust covariance estimation under the approximate factor model with observed factors. We propose a novel framework to first estimate the initial joint covariance matrix of the observed data and the factors, and then…

We consider the fitting of heavy tailed data and distribution with a special attention to distributions with a non--standard shape in the "body" of the distribution. To this end we consider a dense class of heavy tailed distributions…

We study the algorithmic problem of estimating the mean of heavy-tailed random vector in $\mathbb{R}^d$, given $n$ i.i.d. samples. The goal is to design an efficient estimator that attains the optimal sub-gaussian error bound, only assuming…

We consider the problem of streaming kernel regression, when the observations arrive sequentially and the goal is to recover the underlying mean function, assumed to belong to an RKHS. The variance of the noise is not assumed to be known.…

Estimation of the extreme value index under right censoring is a fundamental problem in extreme value theory, with important applications in finance, insurance, and reliability. Classical integral estimators for Pareto-type tails typically…

Standard maximum likelihood or Bayesian approaches to parameter estimation for stochastic differential equations are not robust to perturbations in the continuous-in-time data. In this paper, we give a rather elementary explanation of this…

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…

While distributed parameter estimation has been extensively studied in the literature, little has been achieved in terms of robust analysis and tuning methods in the presence of disturbances. However, disturbances such as measurement noise…

This paper explores the applications of the 20/60/20 rule-a heuristic method that segments data into top-performing, average-performing, and underperforming groups-in mathematical finance. We review the statistical foundations of this rule…

In this paper we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture…

The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…

Online controlled experiments play a crucial role in enabling data-driven decisions across a wide range of companies. Variance reduction is an effective technique to improve the sensitivity of experiments, achieving higher statistical power…

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.…

In statistical inference, we commonly assume that samples are independent and identically distributed from a probability distribution included in a pre-specified statistical model. However, such an assumption is often violated in practice.…