Related papers: Bridging centrality and extremity: Refining empiri…

We consider a general statistical estimation problem involving a finite-dimensional target parameter vector. Beyond an internal data set drawn from the population distribution, external information, such as additional individual data or…

Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…

Estimating spatial extremes from sparse observational networks produces uncertain return level maps, but dense output from physics-based simulation models is often available as a complementary data source. We develop a two-stage frequentist…

One potential solution to combat the scarcity of tail observations in extreme value analysis is to integrate information from multiple datasets sharing similar tail properties, for instance, a common extreme value index. In other words, for…

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme…

The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth…

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…

We present single imputation method for missing values which borrows the idea of data depth---a measure of centrality defined for an arbitrary point of a space with respect to a probability distribution or data cloud. This consists in…

The purpose of this article is to extend the notion of statistical depth to the case of sample paths of a Markov chain. Initially introduced to define a center-outward ordering of points in the support of a multivariate distribution, depth…

Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…

During the past two decades there has been a lot of interest in developing statistical depth notions that generalize the univariate concept of ranking to multivariate data. The notion of depth has also been extended to regression models and…

Nonparametric regression quantiles obtained by inverting a kernel estimator of the conditional distribution of the response are long established in statistics. Attention has been, however, restricted to ordinary quantiles staying away from…

We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the…

The coarse spatial resolution of gridded climate models, such as general circulation models, limits their direct use in projecting socially relevant variables like extreme precipitation. Most downscaling methods estimate the conditional…

Understanding the complex structure of multivariate extremes is a major challenge in various fields from portfolio monitoring and environmental risk management to insurance. In the framework of multivariate Extreme Value Theory, a common…

Analysis and processing of data is a vital part of our modern society and requires vast amounts of computational resources. To reduce the computational burden, compressing and approximating data has become a central topic. We consider the…

Extremes play a special role in Anomaly Detection. Beyond inference and simulation purposes, probabilistic tools borrowed from Extreme Value Theory (EVT), such as the angular measure, can also be used to design novel statistical learning…

The statistical modeling of discrete extremes has received less attention than their continuous counterparts in the Extreme Value Theory (EVT) literature. One approach to the transition from continuous to discrete extremes is the modeling…

In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies with determining which subsets of variables can take…

Anomaly detection is a branch of data analysis and machine learning which aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…