Related papers: Generalized Logistic Models and its orthant tail d…
Generalized linear (GL-) statistics are defined as functionals of an U-quantile process and unify different classes of statistics such as U-statistics and L-statistics. We derive a central limit theorem for GL-statistics of strongly mixing…
Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any time-series and has applications in climate, finance, sports, all the way…
We study the consistency and weak convergence of the conditional tail function and conditional Hill estimators under broad dependence assumptions for a heavy-tailed response sequence and a covariate sequence. Consistency is established…
A new class of bivariate distributions is introduced that extends the Generalized Marshall-Olkin distributions of Li and Pellerey (2011). Their dependence structure is studied through the analysis of the copula functions that they induce.…
It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…
It is well known that the probability distribution of high-frequency financial returns is characterized by a leptokurtic, heavy-tailed shape. This behavior undermines the typical assumption of Gaussian log-returns behind the standard…
Measures of tail dependence between random variables aim to numerically quantify the degree of association between their extreme realizations. Existing tail dependence coefficients (TDCs) are based on an asymptotic analysis of relevant…
In this paper, we introduce a bivariate exponentaited generalized Weibull-Gompertz distribution. The model introduced here is of Marshall-Olkin type. Several properties are studied such as bivariate probability density function and it is…
Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide…
Generalized linear mixed models are powerful tools for analyzing clustered data, where the unknown parameters are classically (and most commonly) estimated by the maximum likelihood and restricted maximum likelihood procedures. However,…
At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…
We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are generalizations of conditional independence models, where the dependence among observed variables is…
We study distributional robustness in the context of Extreme Value Theory (EVT). We provide a data-driven method for estimating extreme quantiles in a manner that is robust against incorrect model assumptions underlying the application of…
We propose an approach to compute the conditional moments of fat-tailed phenomena that, only looking at data, could be mistakenly considered as having infinite mean. This type of problems manifests itself when a random variable Y has a…
We introduce a general class of continuous univariate distributions with positive support obtained by transforming the class of two-piece distributions. We show that this class of distributions is very flexible, easy to implement, and…
Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by…
We tackle the modeling of threshold exceedances in asymptotically independent stochastic processes by constructions based on Laplace random fields. These are defined as Gaussian random fields scaled with a stochastic variable following an…
Estimating the probability of extreme events involving multiple risk factors is a critical challenge in fields such as finance and climate science. This paper proposes a semi-parametric approach to estimate the probability that a…
Many real-world prediction tasks have outcome variables that have characteristic heavy-tail distributions. Examples include copies of books sold, auction prices of art pieces, demand for commodities in warehouses, etc. By learning…
It is well-known that the expected scaled maximum of non-negative random variables with unit mean defines a stable tail dependence function associated with some extreme-value copula. In the special case when these random variables are…