Applied Nonparametric Regression Methods as Alternatives to the Linear Regression Methods (Comparative Study)

Abstract

Linear regression methods impose strong constraints on regression models, especially on the error terms where it assumes that it is independent and follows normal distribution, and this may not be satisfied in many studies, leading to bias that cannot be ignored from the actual model, which affects the credibility of the study.

We present in this paper the problem of estimating the regression function using the Nadarya Watson kernel and k- nearest neighbor estimators as alternatives to the parametric linear regression estimators through a simulation study on an imposed model, where we conducted a comparative study between these methods using the statistical   programming language R in order to know the best of these estimations. Where the mean squares errors (MSE) was used to determine the best estimate.

The results of the simulation study also indicate the effectiveness and efficiency of the nonparametric in the representation of the regression function as compared to linear regression estimators, and indicate the convergence of the performance of these two estimates.