A comparison Study Between the Nadaraya-Watson and the Reweighted Nadaraya-Watson Estimators of the Regression Mean Function

Abstract:

Nonparametric kernel estimators are widely used in regression estimation. One of the most important kernel estimators of the regression mean function is the Nadaraya-Watson estimator.  Another estimator, which is called the Reweighted Nadaraya-Watson estimator has been proposed to improve the performance of the Nadaraya-Watson estimator.  In this paper, we have compared theoretically between the two estimators by looking at their asymptotic bias, variance and the mean squared error. The results of this comparison indicated that the bias of the Reweighted Nadaraya-Watson estimator is better than that of the Nadaraya-Watson estimator.

Also, a comparison of the practical performance of the two estimators based on simulated and real data has been given. The results of this comparison was consistent with the results of the theoretical comparison and indicated that, the Reweighted Nadaraya-Watson estimator has modified the weakness of the Nadaraya-Watson estimator.