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.