  We present a nonparametric family of estimators for the tail index of a
Pareto-type distribution when covariate information is available. Our
estimators are based on a weighted sum of the log-spacings between some
selected observations. This selection is achieved through a moving window
approach on the covariate domain and a random threshold on the variable of
interest. Asymptotic normality is proved under mild regularity conditions and
illustrated for some weight functions. Finite sample performances are presented
on a real data study.
