The semiparametric normal variance-mean mixture model

We study the normal variance-mean mixture model from a semiparametric point of view, i.e. we let the mixing distribution belong to a non-parametric fa mily. The main results are consistency of the non-parametric maximum likeli hood estimator and construction of an asymptotically normal and efficient e stimator for the Euclidian part of the parameter. We study the model accord ing to the theory outlined in the monograph by Bickel et al, (1993) and app ly a general result (based on the theory of empirical processes) for semipa rametric models from van der Vaart (1996) to prove asymptotic normality and efficiency of the proposed estimator.