Estimation of the error distribution function for partial linear single-index models

Abstract

We consider the estimation of the error distribution function of partial linear single-index models. The estimation methods for the error distribution function based on the classical empirical distribution function as well as empirical likelihood method are discussed, the latter method allows for incorporation of additional information on the error distribution function into estimation. We show weak convergence of the corresponding empirical processes to Gaussian processes and compare both approaches with the asymptotic theory and by means of simulation studies.