2003, Volume 65, Pt. 3, 660--670
Designing Experiments For Multi-Variable B-Spline Models
D.C. WOODS, S.M. LEWIS, University of Southampton, Southampton, UK and
J.N. DEWYNNE, University of Oxford, Oxford, UK
SUMMARY. In a range of practical applications where a response cannot be adequately described by a low order polynomial, B-spline regression models for a single variable have proved useful for prediction. In this paper identifiable models for several explanatory variables are considered which are formulated from B-spline and monomial basis functions of known degree and with specified knots. The use of search methods to find efficient designs under the $V$-, $G$- and $D$-optimality criteria is investigated. Two methods of constructing lists of feasible candidate points are described and compared across a variety of examples.
AMS (1991) subject classification. 62K20, 62K05.
Key words and phrases. B-spline basis, optimal design, response surface, search algorithm.