All-bias designs for polynomial spline regression models

Woods, David C. and Lewis, Susan M. (2006) All-bias designs for polynomial spline regression models. Australian & New Zealand Journal of Statistics, 48 (1), 49-58. (doi:10.1111/j.1467-842X.2006.00424.x).

Record type: Article

Abstract

Polynomial spline regression models of low degree have proved useful in modeling responses from designed experiments in science and engineering when simple polynomial models are inadequate. Where there is uncertainty in the number and location of the knots, or breakpoints, of the spline, then designs that minimize the systematic errors resulting from model misspecification may be appropriate. This paper gives a method for constructing such all-bias designs for a single variable spline when the distinct knots in the assumed and true models come from some specified set. A class of designs is defined in terms of the inter-knot intervals and sufficient conditions are obtained for a design within this class to be all-bias under linear, quadratic and cubic spline models. An example of the construction of all-bias designs is given.

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