An improved kernel regression method based on Taylor expansion

Many regression functions obtained by nonparametric regression method often appear inconsonance between smoothness and fitness. This phenomenon is extremely outstanding near the vertex regions. How to improve the fitness and smoothness simultaneously becomes an important problem in the nonparametric regression field. In this paper, an improved kernel regression is proposed by introducing second derivative estimation into kernel regression function based on Taylor expansion theorem. Experimental results on regression problems show that this new method is feasible and enables us to get regression function that is both smooth and well-fitting. The application of the method to grey image enhancement indicates that this approach is fruitful to the enhancement of weak information in the images.