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The circular quantile residual

Author

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  • Andrade, Ana C.C.
  • Pereira, Gustavo H.A.
  • Artes, Rinaldo

Abstract

Circular-linear regression is often used to model the relationship between a circular dependent variable and a set of linear predictor variables. It is used in many areas such as meteorology, biology, and medicine. For checking model adequacy, it is desirable to use residuals that are approximately standard normally distributed. Most of the residuals used in circular regression models do not meet this requirement and are used especially for outlier identification. Other residuals are limited to the von Mises regression models. An asymptotically standard normally distributed residual that can be used for any parametric circular-linear regression model is introduced. Monte Carlo simulation studies suggest that the distribution of this residual is well approximated by the standard normal distribution in small samples. To study the behavior of this residual, two regression models are introduced, and two applications are used to show that the proposed residual can detect model misspecification.

Suggested Citation

  • Andrade, Ana C.C. & Pereira, Gustavo H.A. & Artes, Rinaldo, 2023. "The circular quantile residual," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:csdana:v:178:y:2023:i:c:s016794732200192x
    DOI: 10.1016/j.csda.2022.107612
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    1. SenGupta, Ashis & Kim, Sungsu & Arnold, Barry C., 2013. "Inverse circular–circular regression," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 200-208.
    2. Moritz N. Lang & Lisa Schlosser & Torsten Hothorn & Georg J. Mayr & Reto Stauffer & Achim Zeileis, 2020. "Circular regression trees and forests with an application to probabilistic wind direction forecasting," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1357-1374, November.
    3. S. Liu & T. Ma & A. SenGupta & K. Shimizu & M.-Z. Wang, 2017. "Influence Diagnostics in Possibly Asymmetric Circular-Linear Multivariate Regression Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 76-93, May.
    4. Arthur Pewsey & Eduardo García-Portugués, 2021. "Rejoinder on: Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 76-82, March.
    5. Marco Di Marzio & Agnese Panzera & Charles C. Taylor, 2013. "Non-parametric Regression for Circular Responses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 238-255, June.
    6. Juliana Scudilio & Gustavo H. A. Pereira, 2020. "Adjusted quantile residual for generalized linear models," Computational Statistics, Springer, vol. 35(1), pages 399-421, March.
    7. Gill, Jeff & Hangartner, Dominik, 2010. "Circular Data in Political Science and How to Handle It," Political Analysis, Cambridge University Press, vol. 18(3), pages 316-336, July.
    8. Patricia Espinheira & Silvia Ferrari & Francisco Cribari-Neto, 2008. "On beta regression residuals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(4), pages 407-419.
    9. Umbach, Dale & Jammalamadaka, S. Rao, 2009. "Building asymmetry into circular distributions," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 659-663, March.
    10. Francisco A.M. De Souza & Gilberto A. Paula, 2002. "Theory & Methods: Deviance Residuals for an Angular Response," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 44(3), pages 345-356, September.
    11. Toshihiro Abe & Arthur Pewsey, 2011. "Sine-skewed circular distributions," Statistical Papers, Springer, vol. 52(3), pages 683-707, August.
    12. Abe, Toshihiro & Ley, Christophe, 2017. "A tractable, parsimonious and flexible model for cylindrical data, with applications," Econometrics and Statistics, Elsevier, vol. 4(C), pages 91-104.
    13. Rodríguez, Carlos E. & Núñez-Antonio, Gabriel & Escarela, Gabriel, 2020. "A Bayesian mixture model for clustering circular data," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    14. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    15. Sungsu Kim & Md Monjurul Islam Rifat, 2021. "Diagnostic analysis of a circular-circular regression model using asymmetric or asymmetric bi-modal circular errors," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(12), pages 2848-2858, June.
    16. Shogo Kato & M. C. Jones, 2015. "A tractable and interpretable four-parameter family of unimodal distributions on the circle," Biometrika, Biometrika Trust, vol. 102(1), pages 181-190.
    17. Davide Buttarazzi & Giuseppe Pandolfo & Giovanni C. Porzio, 2018. "A boxplot for circular data," Biometrics, The International Biometric Society, vol. 74(4), pages 1492-1501, December.
    18. Limei Cao & Didong Li & Erchuan Zhang & Zhenning Zhang & Huafei Sun, 2014. "A Statistical Cohomogeneity One Metric on the Upper Plane with Constant Negative Curvature," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-6, December.
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