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This paper introduces the partial Gini covariance, a novel dependence measure that addresses the challenges of high-dimensional inference with heavy-tailed errors, often encountered in fields like finance, insurance, climate, and biology.…
We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…
We revisit and refine known tail inequalities and confidence bounds for the hypergeometric distribution, i.e., for the setting where we sample without replacement from a fixed population with binary values or properties. The results are…
We consider a nonlinear polynomial regression model in which we wish to test the null hypothesis of structural stability in the regression parameters against the alternative of a break at an unknown time. We derive the extreme value…
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…
Language models are increasingly capable and are being rapidly deployed on a population-level scale. As a result, the safety of these models is increasingly high-stakes. Fortunately, advances in alignment have significantly reduced the…
We consider a model for multivariate data with heavy-tailed marginal distributions and a Gaussian dependence structure. The different marginals in the model are allowed to have non-identical tail behavior in contrast to most popular…
Most extreme events in real life can be faithfully modeled as random realizations from a Generalized Pareto distribution, which depends on two parameters: the scale and the shape. In many actual situations, one is mostly concerned with the…
We propose the Cyclic Permutation Test (CPT) to test general linear hypotheses for linear models. This test is non-randomized and valid in finite samples with exact Type I error $\alpha$ for an arbitrary fixed design matrix and arbitrary…
Motivated by the empirical observation of power-law distributions in the credits (e.g., ``likes'') of viral posts in social media, we introduce a high-dimensional tail index regression model and propose methods for estimation and inference…
Auto-calibration is an important property of regression functions for actuarial applications. Comparably little is known about statistical testing of auto-calibration. Denuit et al.~(2024) recently published a test with an asymptotic…
Design and operation of complex engineering systems rely on reliability optimization. Such optimization requires us to account for uncertainties expressed in terms of compli-cated, high-dimensional probability distributions, for which only…
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
This paper attempts to provide a decision-theoretic foundation for the measurement of economic tail risk, which is not only closely related to utility theory but also relevant to statistical model uncertainty. The main result is that the…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating…
Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts,…
In bioequivalence design, power analyses dictate how much data must be collected to detect the absence of clinically important effects. Power is computed as a tail probability in the sampling distribution of the pertinent test statistics.…
This paper provides a specification test for semiparametric models with nonparametrically generated regressors. Such variables are not observed by the researcher but are nonparametrically identified and estimable. Applications of the test…
We develop a Monte Carlo-free approach to inference post output from randomized algorithms with a convex loss and a convex penalty. The pivotal statistic based on a truncated law, called the selective pivot, usually lacks closed form…