Orientation relationship in finite dimensional space. (English) Zbl 1459.62237
The authors consider regression of a point on the surface of the unit sphere in \(d\) dimensions given a point on the surface of the unit sphere in \(p\) dimensions, where \(p\) may not be equal to \(d\), using Möbius transformations as mentioned in [S. Kato and M. C. Jones, J. Am. Stat. Assoc. 105, No. 489, 249–262 (2010; Zbl 1397.60035)]. Point projection is added to the rotation and linear transformation for the regression link function. The parametric model, the local constant and local linear nonparametric models are compared with respect to the \(D\) measure based on all observations. A very illustrative example is given.
Reviewer: Rózsa Horváth-Bokor (Budakalász)
MSC:
| 62R30 | Statistics on manifolds |
| 62H11 | Directional data; spatial statistics |
| 62J12 | Generalized linear models (logistic models) |
Keywords:
orientation of point; exit distribution; geodesic distance; Möbius transformation; projective linear transformation; von Mises-Fisher distributionCitations:
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