Penalized semiparametric density estimation

In this article we propose a penalized likelihood approach for the semiparametric density model with parametric and nonparametric components. An efficient iterative procedure is proposed for estimation. Approximate generalized maximum likelihood criterion from Bayesian point of view is derived for selecting the smoothing parameter. The finite sample performance of the proposed estimation approach is evaluated through simulation. Two real data examples, suicide study data and Old Faithful geyser data, are analyzed to demonstrate use of the proposed method.