论文标题
嘈杂实验设计的数值统计风扇
The numerical statistical fan for noisy experimental designs
论文作者
论文摘要
多项式模型的可识别性是多元回归的关键要求。我们考虑了所谓的统计风扇的类似物，即所有最大可识别层次模型的集合，用于嘈杂的实验设计或具有给定公差矢量的协变量向量。这引起了数值统计风扇的定义。它包括所有最大层次模型，避免模型项的线性依赖性近似。我们开发了一种算法来计算数值统计风扇，该算法使用代数领域的设计理想的所有边界底座计算的最新结果。这些想法应用于热喷涂过程中的数据。事实证明，数值统计风扇有效地计算，并且比各自的统计风扇小得多。获得的对所有稳定可识别层次结构模型的空间的知识增强了，可以改进模型选择程序。
Identifiability of polynomial models is a key requirement for multiple regression. We consider an analogue of the so-called statistical fan, the set of all maximal identifiable hierarchical models, for cases of noisy experimental designs or measured covariate vectors with a given tolerance vector. This gives rise to the definition of the numerical statistical fan. It includes all maximal hierarchical models that avoid approximate linear dependence of the model terms. We develop an algorithm to compute the numerical statistical fan using recent results on the computation of all border bases of a design ideal from the field of algebra. The ideas are applied to data from a thermal spraying process. It turns out that the numerical statistical fan is effectively computable and much smaller than the respective statistical fan. The gained enhanced knowledge of the space of all stable identifiable hierarchical models enables improved model selection procedures.
