Fast Estimation of Multidimensional Regression Functions

Various methods for fitting an unknown functions from the set of noisy measurements are applicable to a wide variety of problems. Among them, the nonparametric algorithms based on the Parzen kernel are willingly used. In the article, we propose a novel and very effective numerical simplification in Parzen approach leading to a significant reduction in computation time. The algorithm is basically developed for multidimensional case. The two-dimensional version of the method is explained in details and analysed. Computational complexity and speed of convergence of the algorithm are studied. Some applications for solving real problems with our algorithms are presented.