Search

We consider the estimation of an extreme conditional quantile. In a first part, we propose a new tail condition in order to establish the asymptotic distribution of an extreme conditional quantile estimator. Next, a general class of estimators is introduced, which encompasses, among others, kernel or nearest neighbors types of estimators. A unified theorem of the asymptotic normality for this general class of estimators is provided under the new tail condition and illustrated on the different well-known examples. A comparison between different estimators belonging to this class is provided on a small simulation study and illustrated on a real dataset on earthquake magnitudes. [ABSTRACT FROM AUTHOR]

We consider bias-reduced estimation of the extreme value index in conditional Pareto-type models with random covariates when the response variable is subject to random right censoring. The bias-correction is obtained by fitting the extended Pareto distribution locally to the relative excesses over a high threshold using the maximum likelihood method. Convergence in probability and asymptotic normality of the estimators are established under suitable assumptions. The finite sample behaviour is illustrated with a simulation experiment and the method is applied to two real datasets. [ABSTRACT FROM AUTHOR]

Recently, the topic of extreme value under random censoring has been considered. Different estimators for the index have been proposed (see Beirlant et al., 2007). All of them are constructed as the classical estimators (without censoring) divided by the proportion of non censored observations above a certain threshold. Their asymptotic normality was established by Einmahl et al. (2008). An alternative approach consists of using the Peaks-Over-Threshold method (Balkema and de Haan, 1974; Smith, 1987) and to adapt the likelihood to the context of censoring. This leads to ML-estimators whose asymptotic properties are still unknown. The aim of this article is to propose one-step approximations, based on the Newton-Raphson algorithm. Based on a small simulation study, the one-step estimators are shown to be close approximations to the ML-estimators. Also, the asymptotic normality of the one-step estimators has been established, whereas in case of the ML-estimators it is still an open problem. The proof of our result, whose approach is new in the Peaks-Over-Threshold context, is in the spirit of Lehmann's theory (1991). [ABSTRACT FROM AUTHOR]

We consider robust and nonparametric estimation of the coefficient of tail dependence in presence of random covariates. The estimator is obtained by fitting the extended Pareto distribution locally to properly transformed bivariate observations using the minimum density power divergence criterion. We establish convergence in probability and asymptotic normality of the proposed estimator under some regularity conditions. The finite sample performance is evaluated with a small simulation experiment, and the practical applicability of the method is illustrated on a real dataset of air pollution measurements. [ABSTRACT FROM AUTHOR]