Related papers: Estimating the mean of a heavy-tailed distribution…
We revisit the estimation of the extreme value index for randomly censored data from a heavy tailed distribution. We introduce a new class of estimators which encompasses earlier proposals given in Worms and Worms (2014) and Beirlant et al.…
This paper addresses the problem of estimating, in the presence of random censoring as well as competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in the heavy-tail case.…
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…
On the basis of Nelson-Aalen nonparametric estimator of the cumulative distribution function, we provide a weak approximation to tail product-limit process for randomly right-censored heavy-tailed data. In this context, a new consistent…
We investigate the estimation of the extreme value index when the data are subject to random censorship. We prove, in a unified way, detailed asymptotic normality results for various estimators of the extreme value index and use these…
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…
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 use bias-reduced estimators of high quantiles, of heavy-tailed distributions, to introduce a new estimator of the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked,…
Estimation of the extreme value index under right censoring is a fundamental problem in extreme value theory, with important applications in finance, insurance, and reliability. Classical integral estimators for Pareto-type tails typically…
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…
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…
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…
Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…
The subject of tail estimation for randomly censored data from a heavy tailed distribution receives growing attention, motivated by applications for instance in actuarial statistics. The bias of the available estimators of the extreme value…
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…
A new approach based on censoring and moment criterion is introduced for parameter estimation of count distributions when the probability generating function is available even though a closed form of the probability mass function and/or…
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…
This article deals with the hypothesis test for the extremely heavy-tailed distributions with infinite mean or variance by using a truncated sample mean. We obtain three necessary and sufficient conditions under which the asymptotic…
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…
In extreme value analysis, the extreme value index plays a vital role as it determines the tail heaviness of the underlying distribution and is the primary parameter required for the estimation of other extreme events. In this paper, we…