Modification of the adaptive Nadaraya-Watson kernel method for nonparametric regression (simulation study)

In this research, a new improvement of the Nadaraya-Watson kernel non parametric regression estimator is proposed and the bandwidth of this new improvement is obtained depending on the three different statistical indicators: robust mean, median and harmonic mean of kernel function instead of using geometric and arithmetic mean, or R. Simulation study is presented, including comparisons with four others Nadaraya-Watson kernel estimators (classical methods). The proposed estimator in the case of harmonic mean is more accurate than all classical methods for all simulations based on MSE criteria.

Automated summary

This research proposes a new improvement for the Nadaraya-Watson kernel nonparametric regression estimator. The bandwidth of this improvement is obtained based on statistical indicators such as robust mean, median, and harmonic mean of kernel function. Simulation study shows that the proposed estimator, especially when using harmonic mean, outperforms classical methods in terms of accuracy.