Application of the Scaling Functions to Nonparametric Regression

For estimating regression function we can use many proceedings. In this paper, we have chosen to apply scaling functions to the estimation of regression functions. When one knows many bivariate date with the values of two variables, in the goal to express a correlation between the two variables we use the regression function. The raw estimator of this function must be "smoothed out" in some way to get a final estimator. For this, we use the scaling functions, examples of such function being the Battle-Lemarié family and Daubechies family. After introducing several notions (multiresolution analysis, filter and projection of function onto approximation spaces), these are applied to obtain the estimators. In the last part, we present the algorithm for estimating nonparametric regression function through the scaling functions.