Related papers: Extreme value statistics for truncated Pareto-type…
We consider estimation of the extreme value index and extreme quantiles for heavy-tailed data that are right-censored. We study a general procedure of removing low importance observations in tail estimators. This trimming procedure is…
We study tail estimation in Pareto-like settings for datasets with a high percentage of randomly right-censored data, and where some expert information on the tail index is available for the censored observations. This setting arises for…
This paper considers estimation and inference about tail features when the observations beyond some threshold are censored. We first show that ignoring such tail censoring could lead to substantial bias and size distortion, even if the…
Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit…
In this paper we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree…
Heavy-tailed distributions are infamously difficult to estimate because their moments tend to infinity as the shape of the tail decay increases. Nevertheless, this study shows the utilization of a modified group of moments for estimating a…
Both parametric distribution functions appearing in extreme value theory - the generalized extreme value distribution and the generalized Pareto distribution - have log-concave densities if the extreme value index gamma is in [-1,0].…
The central limit theorem introduced by Stute [The central limit theorem under random censorship. Ann. Statist. 1995; 23: 422-439] does not hold for some class of heavy-tailed distributions. In this paper, we make use of the extreme value…
A method is described for predicting extremes values beyond the span of historical data. The method - based on extending a curve fitted to a location- and scale-invariant variation of the double-logarithmic QQ-plot - is simple and…
In many applied fields, the prediction of more severe events than those already recorded is crucial for safeguarding against potential future calamities. What-if analyses, which evaluate hypothetical scenarios up to the worst-case event,…
A coupling method is developed for univariate extreme value theory , providing an alternative to the use of the tail empirical/quantile processes. Emphasizing the Peak-over-Threshold approach that approximates the distribution above high…
The extrapolation of extremes to values beyond the span of stationary univariate historical data is considered from Bayesian and Frequentist perspectives. The intention is to make predictions which in some sense "preserve probability". A…
A novel and comprehensive methodology designed to tackle the challenges posed by extreme values in the context of random censorship is introduced. The main focus is on the analysis of integrals based on the product-limit estimator of…
This paper investigates pooling strategies for tail index and extreme quantile estimation from heavy-tailed data. To fully exploit the information contained in several samples, we present general weighted pooled Hill estimators of the tail…
Neural networks are able to approximate any continuous function on a compact set. However, it is not obvious how to quantify the error of the neural network, i.e., the remaining bias between the function and the neural network. Here, we…
The Generalized Pareto Distribution (GPD) plays a central role in modelling heavy tail phenomena in many applications. Applying the GPD to actual datasets however is a non-trivial task. One common way suggested in the literature to…
Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme…
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…
We consider heavy-tailed distributions and compare the well-known estimators of the tail index, based on extreme value theory with a comparatively recent estimator based on a different idea.
Bias reduction in tail estimation has received considerable interest in extreme value analysis. Estimation methods that minimize the bias while keeping the mean squared error (MSE) under control, are especially useful when applying…