ESTIMATIONS OF THE PARTIALLY LINEAR MODELS WITH SMOOTHING SPLINE BASED ON DIFFERENT SELECTION METHODS: A COMPARATIVE STUDY

Abstract

This paper presents a comparative study of different estimations of the partially linear models based on the smoothing spline technique. Performance of this technique greatly depends on the selection of smoothing parameters. Many methods of selecting smoothing parameters such as an improved version of Akaike information criterion (AIC(c)), generalized cross-validation (GCV), cross-validation (CV), Mallows' C-p criterion, risk estimation using classical pilots (REC) and local risk estimation (LRS) are developed in literature. The smoothing parameter selection has been discussed in respect to a smoothing spline implementation in predicting the partially linear model (PLM). To this end, a simulation study has been conducted to evaluate and compare the performance of six selection methods. In this connection, 1000 replications have been performed in simulation for sample sets with different sizes. The AIC(c) method is recommended since it is stable and works well in all simulations. It performs better than other methods especially when the sample sizes are not large.