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.

中文翻译：

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样条小波回归模型的优化设计

在本文中，我们研究了一些小波回归模型的优化设计问题。小波在建模复杂关系方面非常灵活，优化设计作为提高实验精度的一种手段很有吸引力。与 Haar 小波回归模型的设计（Herzberg 和 Traves 1994；Oyet 和 Wiens 2000）相比，我们构建的 I 最优设计不同于 D 最优设计。我们还获得了 c 最优设计。优化（D-和I-）二次样条小波设计被构造，分析和数值。案例研究表明，采用优化设计可以显着节省资源。我们还构建了模型稳健设计，以解决因拟合不完整的小波集而引起的响应错误规范。