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Sample average approximation (SAA) is a widely popular approach to data-driven decision-making under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong asymptotic performance guarantees. Similar guarantees,…

Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…

Real-world measurements often comprise a dominant signal contaminated by a noisy background. Robustly estimating the dominant signal in practice has been a fundamental statistical problem. Classically, mixture models have been used to…

This paper considers the problem of robustly estimating the parameters of a heavy-tailed multivariate distribution when the covariance matrix is known to have the structure of a low-rank matrix plus a diagonal matrix as considered in factor…

In this article, we develop Stein characterization for two-sided tempered stable distribution. Stein characterizations for normal, gamma, Laplace, and variance-gamma distributions already known in the literature follow easily. One can also…

Least absolute deviation regression is applied using a fixed number of points for all values of the index to estimate the index and scale parameter of the stable distribution using regression methods based on the empirical characteristic…

Designing scalable estimation algorithms is a core challenge in modern statistics. Here we introduce a framework to address this challenge based on parallel approximants, which yields estimators with provable properties that operate on the…

The risk premia of traded factors are the sum of factor means and a parameter vector we denote by {\phi} which is identified from the cross section regression of alpha of individual securities on the vector of factor loadings. If phi is…

In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…

Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental problem in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Towards bridging…

Model averaging techniques based on resampling methods (such as bootstrapping or subsampling) have been utilized across many areas of statistics, often with the explicit goal of promoting stability in the resulting output. We provide a…

The key to successful statistical analysis of bivariate extreme events lies in flexible modelling of the tail dependence relationship between the two variables. In the extreme value theory literature, various techniques are available to…

This paper is concerned with particle filtering for $\alpha$-stable stochastic volatility models. The $\alpha$-stable distribution provides a flexible framework for modeling asymmetry and heavy tails, which is useful when modeling financial…

By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These…

Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…

We investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions of optimal subsampling probabilities. One version minimizes the trace of the…

We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion $\alpha$ of contaminating data to guarantee the robustness of the…

We discuss recently developed methods that quantify the stability and generalizability of statistical findings under distributional changes. In many practical problems, the data is not drawn i.i.d. from the target population. For example,…

Based on the methods provided in Caeiro and Gomes (2002) and Fraga Alves (2001), a new class of location invariant Hill-type estimators is derived in this paper. Its asymptotic distributional representation and asymptotic normality are…

Considered here are robust subgroup-classifier learning and testing in change-plane regressions with heavy-tailed errors, which can identify subgroups as a basis for making optimal recommendations for individualized treatment. A new…