Related papers: Scaling conditional tail probability and quantile …
The paper concerns quantile oriented sensitivity analysis. We rewrite the corresponding indices using the Conditional Tail Expectation risk measure. Then, we use this new expression to built estimators.
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 investigate the application of the Adaptive Multilevel Splitting algorithm for the estimation of tail probabilities of solutions of Stochastic Differential Equations evaluated at a given time, and of associated temporal averages. We…
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…
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…
The estimation of conditional quantiles at extreme tails is of great interest in numerous applications. Various methods that integrate regression analysis with an extrapolation strategy derived from extreme value theory have been proposed…
Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the…
Sequential Monte Carlo methods which involve sequential importance sampling and resampling are shown to provide a versatile approach to computing probabilities of rare events. By making use of martingale representations of the sequential…
Heavy tailed distributions present a tough setting for inference. They are also common in industrial applications, particularly with Internet transaction datasets, and machine learners often analyze such data without considering the biases…
We extend known saddlepoint tail probability approximations to multivariate cases, including multivariate conditional cases. Our approximation applies to both continuous and lattice variables, and requires the existence of a cumulant…
We develop an efficient simulation algorithm for computing the tail probabilities of the infinite series $S = \sum_{n \geq 1} a_n X_n$ when random variables $X_n$ are heavy-tailed. As $S$ is the sum of infinitely many random variables, any…
We consider heavy-tailed distributions and compare the well-known estimators of the tail index, based on extreme value theory with a comparatively recent estimator based on a different idea.
We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.
In this paper, we study estimates on tail probabilities $\mathbb{P}(S_r \ge t)$ of several classes of subordinators under mild assumptions on the tail of its L\'evy measure. As an application of that result, we obtain two-sided estimates…
We introduce a new type of estimator for the spectral tail process of a regularly varying time series. The approach is based on a characterizing invariance property of the spectral tail process, which is incorporated into the new estimator…
In this paper we consider the estimation problem for high quantiles of a heavy-tailed distribution from block data when only a few largest values are observed within blocks. We propose estimators for high quantiles and prove that these…
We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation…
In this paper, we consider the problem of estimating an extreme quantile of a Weibull tail-distribution. The new extreme quantile estimator has a reduced bias compared to the more classical ones proposed in the literature. It is based on an…
In this paper we provide a new criterion for the comparison of claims, when we have conditional claims arising in stop loss contracts or contracts with franchise deductible. These stochastic comparisons are made on the basis of the Tail…
In this paper we consider the semi-parametric estimation of extreme quantiles of a right heavy-tail model. We propose a new Log Probability Weighted Moment estimator for extreme quantiles, which is obtained from the estimators of the shape…