Related papers: An Offspring of Multivariate Extreme-Value Theory:…
We derive the maximum bias functions of the MM-estimates and the constrained M-estimates or CM-estimates of regression and compare them to the maximum bias functions of the S-estimates and the $\tau$-estimates of regression. In these…
We prove that if $f:I\subset \Bbb R\to \Bbb R$ is of bounded variation, then the noncentered maximal function $Mf$ is absolutely continuous, and its derivative satisfies the sharp inequality $\|DMf\|_1\le |Df|(I)$. This allows us obtain,…
For an m-dimensional multivariate extreme value distribution there exist 2^{m}-1 exponent measures which are linked and completely characterise the dependence of the distribution and all of its lower dimensional margins. In this paper we…
Extreme environmental phenomena such as major precipitation events manifestly exhibit spatial dependence. Max-stable processes are a class of asymptotically-justified models that are capable of representing spatial dependence among extreme…
Cluster random fields (CRFs) play a crucial role in the study of extremes of stationary regularly varying random fields (RFs). In particular, they appear in the Rosi\'nski representation of max-stable and $\alpha$-stable RFs. In this…
We propose center-outward superquantile and expected shortfall functions, with applications to multivariate risk measurements, extending the standard notion of value at risk and conditional value at risk from the real line to…
We provide a simulation algorithm to simulate from a (multivariate) characteristic function, which is only accessible in a black-box format. The method is based on a generative neural network, whose loss function exploits a specific…
This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…
The classical approach to multivariate extreme value modelling assumes that the joint distribution belongs to a multivariate domain of attraction. This requires each marginal distribution be individually attracted to a univariate extreme…
To quantify the dependence between two random vectors of possibly different dimensions, we propose to rely on the properties of the 2-Wasserstein distance. We first propose two coefficients that are based on the Wasserstein distance between…
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…
Motivated by the Maximum Theorem for convex functions (in the setting of linear spaces) and for subadditive functions (in the setting of Abelian semigroups), we establish a Maximum Theorem for the class of generalized convex functions,…
Max-stability is the property that taking a maximum between two inputs results in a maximum between two outputs. We study max-stability with respect to first-order stochastic dominance, the most fundamental notion of stochastic dominance in…
Take a random variable X with some finite exponential moments. Define an exponentially weighted expectation by E^t(f) = E(e^{tX}f)/E(e^{tX}) for admissible values of the parameter t. Denote the weighted expectation of X itself by r(t) =…
In this paper, we derive optimality conditions (Chebyshev approximation) for multivariate functions. The theory of Chebyshev (uniform) approximation for univariate functions is very elegant. The optimality conditions are based on the notion…
Slepian and Sudakov-Fernique type inequalities, which compare expectations of maxima of Gaussian random vectors under certain restrictions on the covariance matrices, play an important role in probability theory, especially in empirical…
Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a…
We propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based…
(Chern--Simons) vector models exhibit an infinite-dimensional symmetry, the slightly-broken higher-spin symmetry with the unbroken higher-spin symmetry being the first approximation. In this note, we compute the $n$-point correlation…
This paper is devoted to the prediction problem in extreme value theory. Our main result is an explicit expression of the regular conditional distribution of a max-stable (or max-infinitely divisible) process $\{\eta(t)\}_{t\in T}$ given…