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October, 1995 $M$-Estimates of Rigid Body Motion on the Sphere and in Euclidean Space
Ted Chang, Daijin Ko
Ann. Statist. 23(5): 1823-1847 (October, 1995). DOI: 10.1214/aos/1176324325

Abstract

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 $(\nu_1, \ldots, \nu_n)$ are independent with $\nu_i$ symmetrically distributed around $\gamma A \cdot u_i + b, u_i$ known, where the real constant $\gamma > 0, p \times p$ 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.

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Ted Chang. Daijin Ko. "$M$-Estimates of Rigid Body Motion on the Sphere and in Euclidean Space." Ann. Statist. 23 (5) 1823 - 1847, October, 1995. https://doi.org/10.1214/aos/1176324325

Information

Published: October, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0843.62064
MathSciNet: MR1370309
Digital Object Identifier: 10.1214/aos/1176324325

Subjects:
Primary: 62F10
Secondary: 62F12, 62F35, 62H12, 86A60

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 5 • October, 1995
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