Related papers: Inference for heavy-tailed data with Gaussian depe…

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated…

In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…

We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a non-asymptotic point of view. In particular, we define estimators with a…

In situations where both extreme and non-extreme data are of interest, modelling the whole data set accurately is important. In a univariate framework, modelling the bulk and tail of a distribution has been extensively studied before.…

We propose a method to construct a joint statistical model for mixed-domain data to analyze their dependence. Multivariate Gaussian and log-linear models are particular examples of the proposed model. It is shown that the functional…

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

We introduce a new class of multivariate heavy-tailed distributions that are convolutions of heterogeneous multivariate t-distributions. Unlike commonly used heavy-tailed distributions, the multivariate convolution-t distributions embody…

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

A notion of tail dependence based on operator regular variation is introduced for copulas, and the standard tail dependence used in the copula literature is included as a special case. The non-standard tail dependence with marginal power…

We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…

We develop an econometric framework integrating heavy-tailed Student's $t$ distributions with behavioral probability weighting while preserving infinite divisibility. Using 432{,}752 observations across 86 assets (2004--2024), we…

The statistical theory of extremes is extended to observations that are non-stationary and not independent. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial…

Determining the causes of extreme events is a fundamental question in many scientific fields. An important aspect when modelling multivariate extremes is the tail dependence. In application, the extreme dependence structure may…

Finite sample properties of random covariance-type matrices have been the subject of much research. In this paper we focus on the "lower tail" of such a matrix, and prove that it is subgaussian under a simple fourth moment assumption on the…

Regular variation is often used as the starting point for modeling multivariate heavy-tailed data. A random vector is regularly varying if and only if its radial part $R$ is regularly varying and is asymptotically independent of the angular…

If the Euclidean norm is strongly concentrated with respect to a measure, the average distribution of an average marginal of this measure has Gaussian asymptotics that captures tail behaviour. If the marginals of the measure have…

We propose a residual randomization procedure designed for robust Lasso-based inference in the high-dimensional setting. Compared to earlier work that focuses on sub-Gaussian errors, the proposed procedure is designed to work robustly in…

In this paper we introduce and study several multivariate, heavy-tailed distribution classes, and we explore their closure properties and their applications. We consider the class of multivariate, positively decreasing distributions, and…

Forecasting multivariate time series is a computationally intensive task challenged by extreme or redundant samples. Recent resampling methods aim to increase training efficiency by reweighting samples based on their running losses.…

This book chapter illustrates how to apply extreme value statistics to financial time series data. Such data often exhibits strong serial dependence, which complicates assessment of tail risks. We discuss the two main approches to tail risk…