Partially linear models based on heavy-tailed and asymmetrical distributions

In this paper, we provide an extension for partially linear models (PLMs) to allow the errors to follow a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric as well as lightly/heavily tailed distributions which can be used to model datasets with outlying and also atypical data. Using a suitable hierarchical representation of the TP-SMN family developed specifically for PLM, we derived an EM-type algorithm for iteratively computing maximum penalized likelihood estimates of the proposed model parameters. We examined the performance of the proposed PLM model and methodology using simulation studies and a real dataset to show the robust aspects of this model.