On the Kernel Estimation of the Regression Function

Abstract

In this study, we examined the relationship between the independent x and dependent y variables, and the axis of this thesis is focused on the method of how we can estimate the regression function, m(x), where m(x) = E(Y │ X = x). We used nonparametric estimation methods, using the local linear (LL) and the NadarayaWatson (NW) kernel estimators, to estimate the regression function, we derived the strong consistency and the asymptotic normality. Also, the optimal problem of bandwidth selection is studied for the two estimators. A theoretical comparison between the two estimators was given. The performance of the two estimators in estimating the regression function was tested using two simulated data. Finally the comparison results proved that local linear kernel estimator is better than Nadaraya-Watson estimators.