Nonparametric estimation of conditional marginal excess moments

Several risk measures have been proposed in the literature, among them marginal mean excess, defined as MMEp=E[{Y(1)−Q1(1−p)}+|Y(2)>Q2(1−p)], provided E|Y(1)|<∞, where (Y(1),Y(2)) denotes a pair of factors, y+≔max(0,y), Qj quantile function Y(j),j∈{1,2}, and p∈(0,1). In this paper we consider generalization measure, random variables main interest are observed together with covariate X∈Rd, Y(1) excess is also power transformed. This leads to concept conditional moment for which an estimator allowing extrapolation outside data range. The asymptotic properties established, using empirical processes arguments combined multivariate extreme value theory. finite sample behavior evaluated by simulation experiment. We apply our method on vehicle insurance customer dataset.