Using Spline Approximation and Local Polynomial Methods to Estimate the Additive Partial Linear Model

Abstract

The Additive partial linear model (APLM) are very useful in multivariate nonparametric regression. This model is used to study various phenomena, including financial, agricultural, economic, medical, and others.It is characterized by flexibility in dealing with it in terms of the number, type and nature of the studied variables in terms of whether they are linear or non-linear variables. It is used to estimate the effects of some linear and nonlinear explanatory variables on the response variable, and two different methods were used to estimate the model, which are the B-Spline approximation method and the Local polynomial estimators method, using the backfitting algorithm. The comparison between the two methods was done by using comparison criteria represented by mean squares error squares. Through the results of the analysis of simulated experiments, it was noted that the Spline approximate method is more efficient than the method of local polynomial estimators.