Related papers: Tail index estimation, concentration and adaptivit…

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…

Extreme quantile treatment effects (eQTEs) measure the causal impact of a treatment on the tails of an outcome distribution and are central for studying rare, high-impact events. Standard QTE methods often fail in extreme regimes due to…

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…

We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in non-parametric regression model with heteroscedastic Gaussian noise. Focusing on the exponentially weighted aggregate, we prove a…

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…

Let $(X_n:n\geq 0)$ be a sequence of i.i.d. r.v.'s with negative mean. Set $S_0=0$ and define $S_n=X_1+... +X_n$. We propose an importance sampling algorithm to estimate the tail of $M=\max \{S_n:n\geq 0\}$ that is strongly efficient for…

This paper discusses the problem of adaptive estimation of a univariate object like the value of a regression function at a given point or a linear functional in a linear inverse problem. We consider an adaptive procedure originated from…

We propose a class of weighted least squares estimators for the tail index of a distribution function with a regularly varying upper tail. Our approach is based on the method developed by \cite{Holan2010} for the Parzen tail index.…

This paper proposes a scoring-rule-based method for ranking predictive distributions in the Fr\'echet domain that is able to distinguish between different tail indices. The approach is built on normalized order statistics and exploits…

This note describes non-asymptotic variance and tail bounds for order statistics of samples of independent identically distributed random variables. Those bounds are checked to be asymptotically tight when the sampling distribution belongs…

Tree ensembles are non-parametric methods widely recognized for their accuracy and ability to capture complex interactions. While these models excel at prediction, they are difficult to interpret and may fail to uncover useful relationships…

For dynamical systems modeled by a Young tower with exponential tails, we prove an exponential concentration inequality for all separately Lipschitz observables of n variables. When tails are polynomial, we prove polynomial concentration…

The distributed Hill estimator is a divide-and-conquer algorithm for estimating the extreme value index when data are stored in multiple machines. In applications, estimates based on the distributed Hill estimator can be sensitive to the…

We derive the tail inequalities between two random variables starting from inequalities between its moment, or more generally between its Lebesgue-Riesz norms, which holds true on certain sets of parameters. We consider some applications…

We prove the consistency of the Power-Law Fit PLFit method proposed by Clauset et al.(2009) to estimate the power-law exponent in data coming from a distribution function with regularly-varying tail. In the complex systems community, PLFit…

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 $\mathbb{G}$.…

At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…

We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral…

To draw inference on serial extremal dependence within heavy-tailed Markov chains, Drees, Segers and Warcho{\l} [Extremes (2015) 18, 369--402] proposed nonparametric estimators of the spectral tail process. The methodology can be extended…

This work deals with the estimation of the extreme value index and extreme quantiles for heavy tailed data,randomly right truncated by another heavy tailed variable. Under mild assumptions and the condition thatthe truncated variable is…