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Inverse circular–circular regression

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  • SenGupta, Ashis
  • Kim, Sungsu
  • Arnold, Barry C.

Abstract

The problem of determining the values of the independent variable given a value of the dependent variable is commonly referred to as the inverse regression problem. This problem is also encountered in real life with circular data and we refer to it in that context as the inverse circular regression problem. For such a problem, we develop distance-based methods, and parametric methods, where we use the von Mises (vM) error distribution and the asymmetric generalized von Mises (AGvM) error distribution. We then present a goodness of fit comparison among distance-based and parametric methods, utilizing a new criterion called the relative circular prediction bias (RCPB) criterion, with real and simulated examples. Real data applications are given from the biological and environmental sciences.

Suggested Citation

  • SenGupta, Ashis & Kim, Sungsu & Arnold, Barry C., 2013. "Inverse circular–circular regression," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 200-208.
    • Handle: RePEc:eee:jmvana:v:119:y:2013:i:c:p:200-208
    DOI: 10.1016/j.jmva.2013.04.011
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    References listed on IDEAS

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    1. T. D. Downs, 2002. "Circular regression," Biometrika, Biometrika Trust, vol. 89(3), pages 683-698, August.
    2. Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053.
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    Cited by:

    1. Fatemeh Hassanzadeh, 2021. "A smoothing spline model for multimodal and skewed circular responses: Applications in meteorology and oceanography," Environmetrics, John Wiley & Sons, Ltd., vol. 32(2), March.
    2. Uesu, Kagumi & Shimizu, Kunio & SenGupta, Ashis, 2015. "A possibly asymmetric multivariate generalization of the Möbius distribution for directional data," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 146-162.
    3. Davy Paindaveine & Thomas Verdebout, 2019. "Inference for Spherical Location under High Concentration," Working Papers ECARES 2019-02, ULB -- Universite Libre de Bruxelles.
    4. Andrade, Ana C.C. & Pereira, Gustavo H.A. & Artes, Rinaldo, 2023. "The circular quantile residual," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).

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