Optimal multiple functional regression analysis using perturbation theory

Abstract

A regression analysis is presented based on several functions. A normalized data are used which enables the usage of magnitude of orders in perturbation theory. The criteria to eliminate unnecessary base functions are derived with the aid of order of magnitudes in perturbations. The analysis generalizes the previous work on polynomial regression of arbitrary orders. Properties of the regression coefficients are outlined via theorems. Numerical tests are conducted to outline the usage of the analysis to eliminate unnecessary functions and obtain a reasonable approximation of the data in a continuous form.

Keywords

• Functional regression
• perturbation analysis
• data approximation