Related papers: Inference for heavy-tailed data with Gaussian depe…
Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the…
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…
In this paper we consider the estimation problem for high quantiles of a heavy-tailed distribution from block data when only a few largest values are observed within blocks. We propose estimators for high quantiles and prove that these…
Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate the tail index parameter. Improving the Hill estimator was…
The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…
We characterise the learning of a mixture of two clouds of data points with generic centroids via empirical risk minimisation in the high dimensional regime, under the assumptions of generic convex loss and convex regularisation. Each cloud…
We show bounds on tail probabilities for quadratic forms in sub-gaussian non-necessarily independent random variables. Our main tool will be estimates of the Luxemburg norms of such forms. This will allow us to formulate the above-mentioned…
Inference over tails is performed by applying only the results of extreme value theory. Whilst such theory is well defined and flexible enough in the univariate case, multivariate inferential methods often require the imposition of…
A common object to describe the extremal dependence of a $d$-variate random vector $X$ is the stable tail dependence function $L$. Various parametric models have emerged, with a popular subclass consisting of those stable tail dependence…
Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…
Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…
Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…
Using the framework of factor models, we establish the general expression of the coefficient of tail dependence between the market and a stock (i.e., the probability that the stock incurs a large loss, assuming that the market has also…
We make use of the empirical process theory to approximate the adapted Hill estimator, for censored data, in terms of Gaussian processes. Then, we derive its asymptotic normality, only under the usual second-order condition of regular…
Fully describing the entire data set is essential in multivariate risk assessment, since moderate levels of one variable can influence another, potentially leading it to be extreme. Additionally, modelling both non-extreme and extreme…
We consider a family of multivariate distributions with heavy-tailed margins and the type I elliptical dependence structure. This class of risks is common in finance, insurance, environmental and biostatistic applications. We obtain the…
Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of…
In this paper we develop a novel inferential approach based on geometric records for estimating the tail index of heavy-tailed distributions. We construct a maximum likelihood estimator for the Pareto model and establish its strong…
A tail empirical process for heavy-tailed and right-censored data is introduced and its Gaussian approximation is established. In this context, a (weighted) new Hill-type estimator for positive extreme value index is proposed and its…
The paper presents an efficient method for simulating the tails of a target variable Z=h(X) which depends on a set of basic variables X=(X_1, ..., X_n). To this aim, variables X_i, i=1, ..., n are sequentially simulated in such a manner…