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Orientation relationship in finite dimensional space

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  • Jayant Jha
  • Atanu Biswas

Abstract

In the present article, we discuss the regression of a point on the surface of a unit sphere in d dimensions given a point on the surface of a unit sphere in p dimensions, where p may not be equal to d. Point projection is added to the rotation and linear transformation for regression link function. The identifiability of the model is proved. Then, parameter estimation in this set up is discussed. Simulation studies and data analyses are done to illustrate the model.

Suggested Citation

  • Jayant Jha & Atanu Biswas, 2020. "Orientation relationship in finite dimensional space," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 1011-1034, September.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:3:p:1011-1034
    DOI: 10.1111/sjos.12479
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    References listed on IDEAS

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    1. Michael Rosenthal & Wei Wu & Eric Klassen & Anuj Srivastava, 2014. "Spherical Regression Models Using Projective Linear Transformations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1615-1624, December.
    2. T. D. Downs, 2003. "Spherical regression," Biometrika, Biometrika Trust, vol. 90(3), pages 655-668, September.
    3. Marco Di Marzio & Agnese Panzera & Charles C. Taylor, 2014. "Nonparametric Regression for Spherical Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 748-763, June.
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