Brief paper: A new approach to linear regression with multivariate splines

Authors:
C. C. de Visser;Q. P. Chu;J. A. Mulder
Affiliations:
Control and Simulation Division, Faculty of Aerospace Engineering, Delft University of Technology, P.O. Box 5058, 2600GB Delft, The Netherlands;Control and Simulation Division, Faculty of Aerospace Engineering, Delft University of Technology, P.O. Box 5058, 2600GB Delft, The Netherlands;Control and Simulation Division, Faculty of Aerospace Engineering, Delft University of Technology, P.O. Box 5058, 2600GB Delft, The Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
2009

Citing 3
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Abstract

A new methodology for creating highly accurate, static nonlinear maps from scattered, multivariate data is presented. This new methodology uses the B-form polynomials of multivariate simplex splines in a new linear regression scheme. This allows the use of standard parameter estimation techniques for estimating the B-coefficients of the multivariate simplex splines. We present a generalized least squares estimator for the B-coefficients, and show how the estimated B-coefficient variances lead to a new model quality assessment measure in the form of the B-coefficient variance surface. The new modeling methodology is demonstrated on a nonlinear scattered bivariate dataset.