Related papers: Total positivity in multivariate extremes
Mendelian randomization (MR) is a method of exploiting genetic variation to unbiasedly estimate a causal effect in presence of unmeasured confounding. MR is being widely used in epidemiology and other related areas of population science. In…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
We consider the minimization over probability measures of the expected value of a random variable, regularized by relative entropy with respect to a given probability distribution. In the general setting we provide a complete…
Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability…
Many causal and structural parameters in economics can be identified and estimated by computing the value of an optimization program over all distributions consistent with the model and the data. Existing tools apply when the data is…
This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…
Let $\{Z(\tau,s), (\tau,s)\in [a,b]\times[0,T]\}$ with some positive constants $a,b,T$ be a centered Gaussian random field with variance function $\sigma^{2}(\tau,s)$ satisfying $\sigma^{2}(\tau,s)=\sigma^{2}(\tau)$. We firstly derive the…
We analyze, from the viewpoint of positivity preservation, certain discretizations of a fundamental partial differential equation, the one-dimensional advection equation with periodic boundary condition. The full discretization is obtained…
The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. EVT supports using semi-parametric models called max-stable distributions…
We present the first minimax risk bounds for estimators of the spectral measure in multivariate linear factor models, where observations are linear combinations of regularly varying latent factors. Non-asymptotic convergence rates are…
Graphical models in extremes have emerged as a diverse and quickly expanding research area in extremal dependence modeling. They allow for parsimonious statistical methodology and are particularly suited for enforcing sparsity in…
This paper unifies and extends results on a class of multivariate Extreme Value (EV) models studied by Hougaard, Crowder, and Tawn. In these models both unconditional and conditional distributions are EV, and all lower-dimensional marginals…
We study parameter estimation in linear Gaussian covariance models, which are $p$-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex…
Positive continuous outcomes with a point mass at zero are prevalent in biomedical research. To model the point mass at zero and to provide marginalized covariate effect estimates, marginalized two part models (MTP) have been developed for…
Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…
In this article, we propose a new class of consistent tests for $p$-variate normality. These tests are based on the characterization of the standard multivariate normal distribution, that the Hessian of the corresponding cumulant generating…
This paper introduces a dynamic formulation of divergence-regularized optimal transport with weak targets on the path space. In our formulation, the classical relative entropy penalty is replaced by a general convex divergence, and terminal…
Impact assessment of natural hazards requires the consideration of both extreme and non-extreme events. Extensive research has been conducted on the joint modeling of bulk and tail in univariate settings; however, the corresponding body of…
Many two-sample problems call for a comparison of two distributions from an exponential family. Density ratio estimation methods provide ways to solve such problems through direct estimation of the differences in natural parameters. The…
Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…