Optimal designs for spline wavelet regression models

•Wavelets are flexible tools for modeling regression responses.•For some spline wavelet models we provide optimal experimental design strategies.•We construct designs both analytically and numerically.•We address the robustness issues arising from fitting an inadequate set of wavelets.•The methods and results are illustrated in a case study.

In this article we investigate the optimal design problem for some wavelet regression models. Wavelets are very flexible in modeling complex relations, and optimal designs are appealing as a means of increasing the experimental precision. In contrast to the designs for the Haar wavelet regression model (Herzberg and Traves 1994; Oyet and Wiens 2000), the I-optimal designs we construct are different from the D-optimal designs. We also obtain c-optimal designs. Optimal (D- and I-) quadratic spline wavelet designs are constructed, both analytically and numerically. A case study shows that a significant saving of resources may be realized by employing an optimal design. We also construct model robust designs, to address response misspecification arising from fitting an incomplete set of wavelets.