We consider semiparametric asymmetric kernel density estimators when the unknown density has support on [ 0, infinity). We provide a unifying framework which contains asymmetric kernel versions of several semiparametric density estimators considered previously in the literature. This framework allows us to use popular parametric models in a nonparametric fashion and yields estimators which are robust to misspecification. We further develop a specification test to determine if a density belongs to a particular parametric family. The proposed estimators outperform rival non- and semiparametric estimators in finite samples and are simple to implement. We provide applications to loss data from a large Swiss health insurer and Brazilian income data.

Keywords : semiparametric density estimation, asymmetric kernel, income distribution, loss distribution, health insurance, specification testing.

JEL : C13, C14.