We characterize EW D-optimal designs as robust designs against unknown parameter values for experiments under a general parametric model with discrete and continuous factors. When a pilot study is available, we recommend sample-based EW D-optimal designs for subsequent experiments. Otherwise, we recommend EW D-optimal designs under a prior distribution for model parameters. We propose an EW ForLion algorithm for finding EW D-optimal designs with mixed factors, and justify that the designs found by our algorithm are EW D-optimal. To facilitate potential users in practice, we also develop a rounding algorithm that converts an approximate design with mixed factors to exact designs with prespecified grid points and the total number of experimental units. By applying our algorithms for real experiments under multinomial logistic models or generalized linear models, we show that our designs are highly efficient with respect to locally D-optimal designs and more robust against parameter value misspecifications.

翻译：我们刻画了EW D-最优设计，将其视为针对具有离散和连续因子的一般参数模型下实验的未知参数值的稳健设计。当有先导研究可用时，我们推荐基于样本的EW D-最优设计用于后续实验。否则，我们推荐在模型参数的先验分布下的EW D-最优设计。我们提出了一种EW ForLion算法，用于寻找具有混合因子的EW D-最优设计，并证明了我们算法找到的设计是EW D-最优的。为了便于潜在用户在实践中应用，我们还开发了一种舍入算法，该算法可将具有混合因子的近似设计转换为具有预指定网格点和实验单元总数的精确设计。通过将我们的算法应用于多项Logistic模型或广义线性模型下的真实实验，我们表明我们的设计相对于局部D-最优设计具有高效率，并且对参数值误设更具稳健性。