Related papers: Yet another breakdown point notion: EFSBP - illust…
We investigate the construction and performance of summation-by-parts (SBP) operators, which offer a powerful framework for the systematic development of structure-preserving numerical discretizations of partial differential equations.…
The task of modeling claim severities is addressed when data is not consistent with the classical regression assumptions. This framework is common in several lines of business within insurance and reinsurance, where catastrophic losses or…
This paper reviews generalized Pareto copulas (GPC), which turn out to be a key to multivariate extreme value theory. Any GPC can be represented in an easy analytic way using a particular type of norm on $\mathbb{R}^d$, called $D$-norm. The…
As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate…
We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the…
In this article, we extend predictor envelope models to settings with multivariate outcomes and multiple, functional predictors. We propose a two-step estimation strategy, which first projects the function onto a finite-dimensional…
We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
In robust statistics, the breakdown point of an estimator is the percentage of outliers with which an estimator still generates reliable estimation. The upper bound of breakdown point is 50%, which means it is not possible to generate…
Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a…
We consider vector fixed point (FP) equations in large dimensional spaces involving random variables, and study their realization-wise solutions. We have an underlying directed random graph, that defines the connections between various…
We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings.…
Locating 3D objects from a single RGB image via Perspective-n-Points (PnP) is a long-standing problem in computer vision. Driven by end-to-end deep learning, recent studies suggest interpreting PnP as a differentiable layer, so that 2D-3D…
Hyperuniformity is the study of stationary point processes with a sub-Poisson variance in a large window. In other words, counting the points of a hyperuniform point process that fall in a given large region yields a small-variance Monte…
Linear regression with normally distributed errors - including particular cases such as ANOVA, Student's t-test or location-scale inference - is a widely used statistical procedure. In this case the ordinary least squares estimator…
The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably…
The concept of statistical depth extends the notions of the median and quantiles to other statistical models. These procedures aim to formalize the idea of identifying deeply embedded fits to a model that are less influenced by…
Distributed systems have been widely used in practice to accomplish data analysis tasks of huge scales. In this work, we target on the estimation problem of generalized linear models on a distributed system with nonrandomly distributed…
This paper introduces a concept for change-point detection based on normalized entropy as a fundamental metric, aiming to overcome the dependence of traditional entropy methods on assumptions about data distribution and absolute scales.…
Population balance framework is a useful tool that can be used to describe size distribution of droplets in a liquid-liquid dispersion. Breakup and coalescence models provide closures for mathematical formulation of the population balance…