Optimal Design of Experiments on Riemannian Manifolds

• 成果类型: Article
• 署名作者: Li, Hang; Del Castillo, Enrique
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2146587
• 发表日期: 2024
• 页码: 875-886
• 关键词: principal-components; factor models; Spectral Distribution; variable selection; ridge-regression; no eigenvalues; large number; asymptotics; Consistency; shrinkage

摘要

The theory of optimal design of experiments has been traditionally developed on an Euclidean space. In this article, new theoretical results and an algorithm for finding the optimal design of an experiment located on a Riemannian manifold are provided. It is shown that analogously to the results in Euclidean spaces, D-optimal and G-optimal designs are equivalent on manifolds, and we provide a lower bound for the maximum prediction variance of the response evaluated over the manifold. In addition, a converging algorithm that finds the optimal experimental design on manifold data is proposed. Numerical experiments demonstrate the importance of considering the manifold structure in a designed experiment when present, and the superiority of the proposed algorithm. for this article are available online.