Semiparametric inference with kernel likelihood

Abstract

We study a class of semiparametric likelihood models in which parameters are incorporated explicitly, with the unknown likelihood specified nonparametrically by the kernel estimator. The maximum likelihood estimator (MLE) under this semiparametric model is used for inference of the parameters. The method is a generalisation of the semiparametric regression model we proposed recently. Such semiparametric models are robust, and MLEs under these likelihoods are shown to be consistent, asymptotic normal with rate √n and possess Wilks property.