Finding partial and global optimal combinations for generalized non-parametric regressions

Nonparametric regression plays a central role in data fitting and analysis. Numerous well-established techniques and algorithms have been developed for constructing nonparametric regression models. Among them, kernel-based methods form a particularly intuitive class, as they exploit locality, kernel functions, and window widths to fit data. In this study, we develop a generalized model that encompasses most standard kernel estimators. This generalization enables systematic exploration of optimal parameter choices to improve fitting performance, and it also provides a unified framework for examining various existing kernel regression methods. We conduct extensive experiments on both real and simulated datasets to evaluate and compare the effectiveness of the proposed model. The results show that our model is consistent with typical kernel regression settings and remains compatible with other analytical tools. When combined with additional learning techniques, these theoretical developments and applications can be further integrated into the broader domain of machine learning.