M-estimates of rigid body motion on the sphere and in Euclidean space

• 成果类型: Article
• 署名作者: Chang, T; Ko, DJ
• 署名单位: Virginia Commonwealth University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324325
• 发表日期: 1995
• 页码: 1823-1847
• 关键词: regression; distributions

摘要

This paper calculates the influence functions and asymptotic distributions of M-estimators of the rotation A in a spherical regression model on the unit sphere in p dimensions with isotropic errors. The problem arises in the reconstruction of the motion of a rigid body on the surface of the sphere. The comparable model for p-dimensional Euclidean space data is that (upsilon(1),...,upsilon(n)) are independent with upsilon(i) symmetrically distributed around gamma A . u(i) + b, u(i) known, where the real constant gamma > 0, p x p rotation matrix A and p-vector b are the parameters to be estimated. This paper also calculates the influence functions and asymptotic distributions of M-estimators for gamma, A and b. Besides rigid body motion, this problem arises in image registration from landmark data. Particular attention is paid to how the geometry of the rigid body or landmarks affects the statistical properties of the estimators.