Related papers: Testing for tail behavior using extreme spacings
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…
Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. Multivariate extremes are usually characterized using parametric models, some of which have simpler submodels at the boundary of their parameter…
Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…
We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test…
Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…
A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the…
The tail index, indicating the degree of fatness of the tail distribution, is an important component of extreme value theory since it dominates the asymptotic distribution of extreme values such as the sample maximum. In this paper, we…
The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual…
Using an intrinsic approach, we study some properties of random fields which appear as tail fields of regularly varying stationary random fields. The index set is allowed to be a general locally compact Hausdorff Abelian group $\mathbb{G}$.…
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…
The analysis of extremal dependence in high dimensions has recently attracted considerable interest. Existing methodology primarily focuses on modeling and estimation of extremal dependence structures, often supported by concentration…
A fundamental problem in high-dimensional testing is that of global null testing: testing whether the null holds simultaneously in all of $n$ hypotheses. The max test, which uses the smallest of the $n$ marginal p-values as its test…
An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without…
We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…
Empirical likelihood is a well-known nonparametric method in statistics and has been widely applied in statistical inference. The method has been employed by Lu and Peng (2002) to constructing confidence intervals for the tail index of a…
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…
We develop goodness-of-fit tests for max-stable random fields, which are used to model heavy-tailed spatial data. The test statistics are constructed based on the Fourier transforms of the indicators of extreme values in the heavy-tailed…
We propose a new testing procedure about the tail weight parameter of multivariate Student $t$ distributions by having recourse to the Le Cam methodology. Our test is asymptotically as efficient as the classical likelihood ratio test, but…
This paper contributes to answering a question that is of crucial importance in risk management and extreme value theory: How to select the threshold above which one assumes that the tail of a distribution follows a generalized Pareto…
The issue of combining individual $p$-values to aggregate multiple small effects is prevalent in many scientific investigations and is a long-standing statistical topic. Many classical methods are designed for combining independent and…