UNIVARIATE AND MULTIVARIATE POLYNOMIAL REGRESSION CONSTRUCTION FROM A REDUNDANT REPRESENTATION USING AN ACTIVE EXPERIMENT

Abstract

We consider the problem of a multidimensional polynomial regression construction from a given redundant representation based on the results of an active experiment. Redundant representation means inclusion in it the members which are possibly absent in the structure of the studied regression. Thus, we have a problem not only to estimate the values of the unknown coefficients of multidimensional polynomial regression from the results of an active experiment, but also to eliminate the redundant members from its redundant representation. The solution to this problem is based on: (a) obtaining new properties of the coefficients of normalized orthogonal polynomials of Forsythe; (b) possibility of reducing the problem of estimating the unknown coefficients for nonlinear members of multivariate polynomial regression to the problem of estimating the coefficients for the set of univariate polynomial regressions and solving the corresponding systems of linear equalities; (c) using the method to eliminate the redundant members of multidimensional nonlinear polynomial regression which organically includes both the methodology of cluster analysis and the main idea of the group method of data handling – dividing the experimental data into two sets, one of which is not used to estimate unknown coefficients of multidimensional polynomial regression given by a redundant representation.