Regression Modeling for Size-and-Shape Data Based on a Gaussian Model for Landmarks

• 成果类型: Article
• 署名作者: Dryden, Ian L.; Kume, Alfred; Paine, Phillip J.; Wood, Andrew T. A.
• 署名单位: University of Nottingham; University of Kent; University of Sheffield; Australian National University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1724115
• 发表日期: 2021
• 页码: 1011-1022
• 关键词: normalizing constant; maximum-likelihood; bingham; distributions; Consistency

摘要

In this article, we propose a regression model for size-and-shape response data. So far as we are aware, few such models have been explored in the literature to date. We assume a Gaussian model for labeled landmarks; these landmarks are used to represent the random objects under study. The regression structure, assumed in this article to be linear in the ambient space, enters through the landmark means. Two approaches to parameter estimation are considered. The first approach is based directly on the marginal likelihood for the landmark-based shapes. In the second approach, we treat the orientations of the landmarks as missing data, and we set up a model-consistent estimation procedure for the parameters using the EM algorithm. Both approaches raise challenging computational issues which we explain how to deal with. The usefulness of this regression modeling framework is demonstrated through real-data examples. Supplementary materials for this article are available online.