摘要：It is well-known that estimating extreme quantiles, namely, quantiles lying beyondthe range of the available data, is a nontrivial problem that involves the analysis oftail behavior through the estimation of the extreme-value index. For heavy-taileddistributions, on which this paper focuses, the extreme-value index is often called thetail index and extreme quantile estimation typically involves an extrapolation procedure.Besides, in various applications, the random variable of interest can be linkedto a random covariate. In such a situation, extreme quantiles and the tail index arefunctions of the covariate and are referred to as conditional extreme quantiles and theconditional tail index, respectively. The goal of this paper is to provide classes of estimatorsof these quantities when there is a functional (i.e. possibly infinite-dimensional)covariate. Our estimators are obtained by combining regression techniques with a generalizationof a classical extrapolation formula. We analyze the asymptotic propertiesof these estimators, and we illustrate the finite-sample performance of our conditionalextreme quantile estimator on a simulation study and on a real chemometric data set.
关键词：heavy-tailed distribution; functional random covariate; extreme quantile; tail index;asymptotic normality.
