Related papers: Robustness and accuracy of methods for high dimens…

We consider the performance of the bootstrap in high-dimensions for the setting of linear regression, where $p<n$ but $p/n$ is not close to zero. We consider ordinary least-squares as well as robust regression methods and adopt a minimalist…

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…

We propose a new testing procedure about the tail weight parameter of multivariate Student $t$ distributions by having recourse to the Le Cam methodology. Our test is asymptotically as efficient as the classical likelihood ratio test, but…

Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $\alpha$-stable distribution received much interest in…

It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…

Signal temporal logic (STL) is a powerful tool for describing complex behaviors for dynamical systems. Among many approaches, the control problem for systems under STL task constraints is well suited for learning-based solutions, because…

The Student-$t$ distribution is widely used in statistical modeling of datasets involving outliers since its longer-than-normal tails provide a robust approach to hand such data. Furthermore, data collected over time may contain censored or…

We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…

Heckman selection model is the most popular econometric model in analysis of data with sample selection. However, selection models with Normal errors cannot accommodate heavy tails in the error distribution. Recently, Marchenko and Genton…

Strict stationarity is a common assumption used in the time series literature in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak…

In a broad class of reinforcement learning applications, stochastic rewards have heavy-tailed distributions, which lead to infinite second-order moments for stochastic (semi)gradients in policy evaluation and direct policy optimization. In…

A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough…

In decision making problems for continuous state and action spaces, linear dynamical models are widely employed. Specifically, policies for stochastic linear systems subject to quadratic cost functions capture a large number of applications…

We consider the task of heavy-tailed statistical estimation given streaming $p$-dimensional samples. This could also be viewed as stochastic optimization under heavy-tailed distributions, with an additional $O(p)$ space complexity…

We develop an econometric framework integrating heavy-tailed Student's $t$ distributions with behavioral probability weighting while preserving infinite divisibility. Using 432{,}752 observations across 86 assets (2004--2024), we…

Robust Bayesian linear regression is a classical but essential statistical tool. Although novel robustness properties of posterior distributions have been proved recently under a certain class of error distributions, their sufficient…

Machine learning has demonstrated remarkable prediction accuracy over i.i.d data, but the accuracy often drops when tested with data from another distribution. In this paper, we aim to offer another view of this problem in a perspective…

Let $T$ be the Student one- or two-sample $t$-, $F$-, or Welch statistic. Now release the underlying assumptions of normality, independence and identical distribution and consider a more general case where one only assumes that the vector…

Real data often contain anomalous cases, also known as outliers. These may spoil the resulting analysis but they may also contain valuable information. In either case, the ability to detect such anomalies is essential. A useful tool for…

Adversarial robustness is a critical challenge in deploying deep neural networks for real-world applications. While adversarial training is a widely recognized defense strategy, most existing studies focus on balanced datasets, overlooking…