A local moment type estimator for the extreme value index in regression with random covariates

This article deals with the nonparametric estimation of the conditional extreme value index of a response in the presence of random covariates. In particular, it is assumed that the conditional response distribution belongs to the max-domain of attraction of the extreme value distribution, and its index is estimated locally within a narrow neighbourhood of the point of interest in the covariate space. The moment estimator, originally introduced in Dekkers, Einmahl, & de Haan (1989), is adjusted to the local estimation context, and its asymptotic properties are investigated under some mild conditions on the response distribution, the density function of the covariates, the kernel function and for appropriately chosen sequences of bandwidth and threshold parameters. The finite sample performance of the proposed estimator is evaluated by means of an extensive simulation study where a comparison with alternatives from the recent literature is provided. We also illustrate the practical applicability of the estimator on the world catalogue of earthquake magnitudes. The Canadian Journal of Statistics 42: 487-507; 2014