Conditional extremes from heavy-tailed distributions: an application to the estimation of extreme rainfall return levels (Q549644)

A nearest neighbor (NN) estimator is proposed for estimation of the conditional tail index \(\gamma(x)\) of a random variable \(Y\) given covariates \(x\), where \(x\) is an element of a metric space \(E\). The estimate is a weighted sum of log-spacings obtained from observations nearest to \(x\) in \(E\). Asymptotic behavior of the obtained estimates is investigated in the case of independent observations. NN versions of the Hill and Zipf estimators are considered as examples. The authors propose a new weighting technique aimed to minimize the asymptotic mean-squared error of the estimate. The behavior of the estimates for dependent observations is investigated via simulations. An application to rainfall data from southern France is presented.