Related papers: Statistical inference for heavy tailed series with…
Heavy-tailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closed-form in graphical models which involve such heavy-tailed distributions. In this work, we…
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…
Let $\{X_t, t \geq 1\}$ be a sequence of identically distributed and pairwise asymptotically independent random variables with regularly varying tails and $\{ \Theta_t, t\geq1 \}$ be a sequence of positive random variables independent of…
In this paper, we study the quasi-stationary behavior of the one-dimensional diffusion process with a regular or exit boundary at 0 and an entrance boundary at $\infty$. By using the Doob's $h$-transform, we show that the conditional…
We develop a testing procedure for distinguishing between a long-range dependent time series and a weakly dependent time series with change-points in the mean. In the simplest case, under the null hypothesis the time series is weakly…
Causal inference for extreme events has many potential applications in fields such as climate science, medicine and economics. We study the extremal quantile treatment effect of a binary treatment on a continuous, heavy-tailed outcome.…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
As alternatives to the normal distributions, $t$ distributions are widely applied in robust analysis for data with outliers or heavy tails. The properties of the multivariate $t$ distribution are well documented in Kotz and Nadarajah's…
The article describes the limiting distribution of the extremes of observations that arrive in clusters. We start by studying the tail behaviour of an individual cluster and then we apply the developed theory to determine the limiting…
We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
It has been shown that some macroeconomic time series, especially those where outliers could be present, can be well modelled using heavy tailed distributions for the noise components. Methods for deciding when and where heavy-tailed models…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…
This paper addresses the statistical problem of estimating the infinite-norm deviation from the empirical mean to the distribution mean for high-dimensional distributions on $\{0,1\}^d$, potentially with $d=\infty$. Unlike traditional…
This paper presents a new model for characterising temporal dependence in exceedances above a threshold. The model is based on the class of trawl processes, which are stationary, infinitely divisible stochastic processes. The model for…
We consider a class of stationary processes exhibiting both long-range dependence and heavy tails. Separate limit theorems for sums and for extremes have been established recently in literature with novel objects appearing in the limits. In…
The task for a general and useful classification of the tail behaviors of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be…
Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…
This paper considers the maximum generalized empirical likelihood (GEL) estimation and inference on parameters identified by high dimensional moment restrictions with weakly dependent data when the dimensions of the moment restrictions and…
We re-visit tail the index regressions framework. For linear specifications, we find that the usual full rank condition can fail because conditioning on extreme outcomes causes regressors to degenerate to constants. Taking this into…