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The key to successful statistical analysis of bivariate extreme events lies in flexible modelling of the tail dependence relationship between the two variables. In the extreme value theory literature, various techniques are available to…
This paper studies the distributed optimization problem under the influence of heavy-tailed gradient noises. Here, a heavy-tailed noise means that the noise does not necessarily satisfy the bounded variance assumption. Instead, it satisfies…
We consider distributed recursive estimation of consensus+innovations type in the presence of heavy-tailed sensing and communication noises. We allow that the sensing and communication noises are mutually correlated while independent…
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…
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…
We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…
The extreme value theory is very popular in applied sciences including Finance, economics, hydrology and many other disciplines. In univariate extreme value theory, we model the data by a suitable distribution from the general max-domain of…
Estimation of the tail index of heavy-tailed distributions and its applications are essential in many research areas. We propose a class of weighted least squares (WLS) estimators for the Parzen tail index. Our approach is based on the…
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…
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…
This paper introduces a flexible framework for the estimation of the conditional tail index of heavy tailed distributions. In this framework, the tail index is computed from an auxiliary linear regression model that facilitates estimation…
Causal inference for extreme events has many potential applications in fields such as climate science, medicine and economics. We study the extremal quantile treatment effect of a binary treatment on a continuous, heavy-tailed outcome.…
Based on suitable left-truncated or censored data, two flexible classes of $M$-estimations of Weibull tail coefficient are proposed with two additional parameters bounding the impact of extreme contamination. Asymptotic normality with…
The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…
Ratios of central order statistics seem to be very useful for estimating the tail of the distributions and therefore, quantiles outside the range of the data. In 1995 Isabel Fraga Alves investigated the rate of convergence of three…
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 consider removing lower order statistics from the classical Hill estimator in extreme value statistics, and compensating for it by rescaling the remaining terms. Trajectories of these trimmed statistics as a function of the extent of…
Modeling and understanding multivariate extreme events is challenging, but of great importance in various applications - e.g. in biostatistics, climatology, and finance. The separating Hill estimator can be used in estimating the extreme…
Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the…
In this article, we present the maximum weighted likelihood estimator (MWLE) for robust estimations of heavy-tail finite mixture models (FMM). This is motivated by the complex distributional phenomena of insurance claim severity data, where…