Nadaraya-Watson (NW) kernel regression estimator is a widely used and flexible nonparametric estimator of a regression function, which is often obtained by using a fixed bandwidth. Several studies showed that the adaptive kernel estimators with varying bandwidths have better performance results. In this paper, a new improvement of the NW kernel regression estimator is proposed and the bandwidth of this new improvement is obtained depending on the range of the observations. Simulated example is presented, including comparisons with three others NW estimators. The performance of the proposed new estimator is evaluated via the MSE criterion. The results of the simulation study were very promising; it shows that our modified NW estimator performs well in all cases.

 

Key words: Nonparametric estimation, smoothing parameter, local bandwidth factor, Nadaraya-Watson kernel regression estimator, modified Nadaraya-Watson (NW) estimator.