Related papers: Tail index estimation, concentration and adaptivit…
The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees, Segers and Warchol [Extremes 18(3): 369--402, 2015] proposed estimators of the marginal distributions of this…
We study split-conformal prediction for regression when the reported prediction set must be a single interval, at target marginal coverage $1-\alpha$, where $\alpha$ is the nominal miscoverage level. Under this reporting constraint, the…
We make use of the empirical process theory to approximate the adapted Hill estimator, for censored data, in terms of Gaussian processes. Then, we derive its asymptotic normality, only under the usual second-order condition of regular…
By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These…
The estimation of the Extreme Value Index (EVI) is fundamental in extreme value analysis but suffers from high variance due to reliance on only a few extreme observations. We propose a control variates based transfer learning approach in a…
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…
We present novel martingale concentration inequalities for martingale differences with finite Orlicz-$\psi_\alpha$ norms. Such martingale differences with weak exponential-type tails scatters in many statistical applications and can be…
We propose a new threshold selection method for the nonparametric estimation of the extremal index of stochastic processes. The so-called discrepancy method was proposed as a data-driven smoothing tool for estimation of a probability…
This article is dedicated to the estimation of the regression function when the explanatory variable is a weakly dependent process whose correlation coefficient exhibits exponential decay and has a known bounded density function. The…
We study the effect of approximation errors in assessing the extreme behavior of heavy-tailed random objects. We give conditions for the approximation error such that the standard asymptotic results hold for the classical Hill estimator and…
The Hill estimator is often used to infer the power behavior in tails of experimental distribution functions. This estimator is known to produce bad results in certain situations which have lead to the so-called Hill horror plots. In this…
We investigate the use of optimization to compute bounds for extremal performance measures. This approach takes a non-parametric viewpoint that aims to alleviate the issue of model misspecification possibly encountered by conventional…
Recently, the concept of tail dependence has been discussed in financial applications related to market or credit risk. The multivariate extreme value theory is a proper tool to measure and model dependence, for example, of large loss…
Model selection is often performed by empirical risk minimization. The quality of selection in a given situation can be assessed by risk bounds, which require assumptions both on the margin and the tails of the losses used. Starting with…
One of the main goal of extreme value analysis is to estimate the probability of rare events given a sample from an unknown distribution. The upper tail behavior of this distribution is described by the extreme value index. We present a new…
In one-dimensional density estimation on i.i.d. observations we suggest an adaptive cross-validation technique for the selection of a kernel estimator. This estimator is both asymptotic MISE-efficient with respect to the monotone oracle,…
We introduce a consistent estimator of the extreme value index under random truncation based on a single sample fraction of top observations from truncated and truncation data. We establish the asymptotic normality of the proposed estimator…
The theory of adaptive estimation and oracle inequalities for the case of Gaussian-shift--finite-interval experiments has made significant progress in recent years. In particular, sharp-minimax adaptive estimators and exact exponential-type…
In this paper, we investigate the extreme-value methodology, to propose an improved estimator of the conditional tail expectation ($CTE$) for a loss distribution with a finite mean but infinite variance. The present work introduces a new…
We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By…