Local Multiplicative Bias Correction for Asymmetric Kernel Density Estimators

We cionsider semiparmetric assymetric kernel density estimators when the unkonwn density has support on [0,∞). We provide a unifying framework which contains assymmetric 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 particular parametic family. The proposed estimators outperform rival non- and semiparmetric estimators and finite samples and are simple to implement. We provide applications to loss data from a large Swiss health insurer and Brazilian income data.