Di Marzio, M, Panzera, A and Taylor, CC orcid.org/0000-0003-0181-1094 (2019) Nonparametric Rotations for Sphere-Sphere Regression. Journal of the American Statistical Association, 114 (525). pp. 466-476. ISSN 0162-1459
Abstract
Regression of data represented as points on a hypersphere has traditionally been treated using parametric families of transformations that include the simple rigid rotation as an important, special case. On the other hand, nonparametric methods have generally focused on modeling a scalar response through a spherical predictor by representing the regression function as a polynomial, leading to component-wise estimation of a spherical response. We propose a very flexible, simple regression model where for each location of the manifold a specific rotation matrix is to be estimated. To make this approach tractable, we assume continuity of the regression function that, in turn, allows for approximations of rotation matrices based on a series expansion. It is seen that the nonrigidity of our technique motivates an iterative estimation within a Newton–Raphson learning scheme, which exhibits bias reduction properties. Extensions to general shape matching are also outlined. Both simulations and real data are used to illustrate the results. Supplementary materials for this article are available online.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 American Statistical Association. This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 19 Jan 2018, available online: http://www.tandfonline.com/10.1080/01621459.2017.1421542. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Fisher's method of scoring; Local smoothing; Singular value decomposition; Skew-symmetric matrices; Spherical kernels; Wahba's problem |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 18 Dec 2017 14:13 |
Last Modified: | 21 May 2019 13:55 |
Status: | Published |
Publisher: | Taylor & Francis |
Identification Number: | 10.1080/01621459.2017.1421542 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:125319 |