Kernel Regression by Mode Calculation of the Conditional Probability Distribution

Regression is a very important method in engineering and science for the estimation of the dependencies between two or more variables on the basis of some given sample points. The best known regression method is certainly the parametric regression technique after Legendre and Gauss, which minimizes the squared error between a model - often a polynom - and the samples. The least squares method is fast and well suitable for strongly linearly correlated data, but seldom appropriate for high-dimensional problems with difficult, unknown, and nonlinear dependencies. For these problems, nonparametric regression techniques - like kernel or Nadaraya-Watson regression methods - are more suitable (Nadaraya [1964], Watson [1964]).