Related papers: Layered Hill estimator for extreme data in cluster…
Many complex networks in natural and social phenomena have often been characterized by heavy-tailed degree distributions. However, due to rapidly growing size of network data and concerns on privacy issues about using these data, it becomes…
This paper establishes the functional convergence of the Extreme Nelson--Aalen and Extreme Kaplan--Meier estimators, which are designed to capture the heavy-tailed behaviour of censored losses. The resulting limit representations can be…
Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. In a directed preferential attachment model, despite the well-known marginal power-law degree…
A measure of primal importance for capturing the serial dependence of a stationary time series at extreme levels is provided by the limiting cluster size distribution. New estimators based on a blocks declustering scheme are proposed and…
We revisit the estimation of the extreme value index for randomly censored data from a heavy tailed distribution. We introduce a new class of estimators which encompasses earlier proposals given in Worms and Worms (2014) and Beirlant et al.…
Even though practitioners often estimate Pareto exponents running OLS rank-size regressions, the usual recommendation is to use the Hill MLE with a small-sample correction instead, due to its unbiasedness and efficiency. In this paper, we…
The subject of tail estimation for randomly censored data from a heavy tailed distribution receives growing attention, motivated by applications for instance in actuarial statistics. The bias of the available estimators of the extreme value…
We study the fundamental task of outlier-robust mean estimation for heavy-tailed distributions in the presence of sparsity. Specifically, given a small number of corrupted samples from a high-dimensional heavy-tailed distribution whose mean…
Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions…
Statistical analysis of extremes can be used to predict the probability of future extreme events, such as large rainfalls or devastating windstorms. The quality of these forecasts can be measured through scoring rules. Locally scale…
When applying multivariate extreme value statistics to analyze tail risk in compound events defined by a multivariate random vector, one often assumes that all dimensions share the same extreme value index. While such an assumption can be…
We develop two new estimators for a general class of stationary GARCH models with possibly heavy tailed asymmetrically distributed errors, covering processes with symmetric and asymmetric feedback like GARCH, Asymmetric GARCH, VGARCH and…
In this paper, we propose an estimator of the second-order parameter of randomly right-truncated Pareto-type distributions data and establish its consistency and asymptotic normality. Moreover, we derive an asymptotically unbiased estimator…
In this survey we present an extensive research of the vast literature about the Generalized Lambda Distribution (GLD) and propose a hurdle, or two-way, model whose associated distribution is the GLD in order to meet the demand for a highly…
In optical non-linear processes rogue waves can be observed, which can be mathematically described by heavy-tailed distributions. These distributions are special due to the fact that the probability of registering extremely high intensities…
We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…
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.…
Extreme U-statistics arise when the kernel of a U-statistic has a high degree but depends only on its arguments through a small number of top order statistics. As the kernel degree of the U-statistic grows to infinity with the sample size,…
Expectile, as the minimizer of an asymmetric quadratic loss function, is a coherent risk measure and is helpful to use more information about the distribution of the considered risk. In this paper, we propose a new risk measure by replacing…
This paper introduces a new distribution to improve tail risk modeling. Based on the classical normal distribution, we define a new distribution by a series of heat equations. Then, we use market data to verify our model.