Abstract
The last 40 years have seen a vigorous development of regression analysis involving circular data. A large body of results and techniques is now disseminated throughout the literature. In this paper, we provide a review of the literature on regressions involving circular variables that will be useful as a unified and up-to-date account of these methods for practical use. Examples and theoretical details are referred to corresponding papers herein, and omitted in our paper. Some of future topics of interest are also provided. Bayesian and non-parametric regression models involving a circular variable(s) are not included in this paper and will appear elsewhere.
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References
Abe, T., & Pewsey, A. (2011). Sine-skewed circular distributions. Statistical Papers, 52, 683–707.
Anderson-Cook, C. M. (2000). A second order model for cylindrical data. Journal of Statistical Computation and Simulation, 66, 51–65.
Arnold, B. C., & Beaver, R. J. (2000). Hidden truncation models. The Indian Journal of Statistics: Series A, 62, 23–35.
Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12, 171–178.
Downs, T. D., & Mardia, K. V. (2002). Circular regression. Biometrika, 89, 683–698.
Fisher, N. I., & Lee, A. J. (1992). Regression models for an angular response. Biometrics, 48, 665–677.
Fisher, N. I., & Powell, C. McA. (1989). Statistical analysis of two-dimensional palaeocurrent data: Methods and examples. Austrian Journal of Earth Sciences, 36, 91–107.
Gould, A. L. (1969). A regression technique for angular variates. Biometrics, 25, 683–700.
Jammalamadaka, S., & SenGupta, A. (2001). Topics in circular statistics. New York: World Scientific.
Johnson, R. A., & Wehrly, T. E. (1978). Bivariate models for dependence of angular observations and a related Markov process. Biometrika, 66, 255–256.
Kim, S. (2009). Inverse circular regression with possibly asymmetric error distribution. Ph.D. Dissertation. University of California, Riverside.
Kim, S., & SenGupta, A. (2012). A three-parameter generalized von Mises distribution. Statistical Papers, 54, 685–693.
Kim, S., & SenGupta, A. (2015). Inverse circular-linear/linear-circular regression. Communications in Statistics: Theory and Methods, 44, 4772–4782.
Kim, S., & SenGupta, A. (2016). Multivariate and multiple circular regression. Journal of Statistical Computation and Simulation, 87, https://doi.org/10.1080/00949655.2016.1261292.
Lund, U. (1999). Least circular distance regression for directional data. Journal of Applied Statistics, 26, 723–733.
Mardia, K. V., & Sutton, T. W. (1978). A model for cylindrical variables with applications. Journal of Royal Statistical Society: Series B, 40, 229–233.
Pewsey, A. (2000). The wrapped skew-normal distribution on the circle. Communications in Statistics: Theory and Methods, 29, 2459–2472.
Sarma, Y. R., & Jammalamadaka, S. (1993). Circular regression. In Proceedings of the Third Pacific Asia Statistical Conference (pp. 109–128).
Schmidt-Koenig, K. (1963). On the role of the loft, the distance and the site of release in pigeon homming. Biological Bulletin, 125, 154–164.
SenGupta, A., Kim, S., & Arnold, B. C. (2013). Inverse circular-circular regression. Journal of Multivariate Analysis, 119, 200–208.
SenGupta, A., & Kim, S. (2016). Statistical inference for homologous gene pairs between two circular genomes: A new circular-circular regression model. Statistical Methods and Applications, 25, 421–432.
SenGupta, A., & Ugwuowo, F. I. (2006). Asymmetric circular-linear multivariate regression models with applications to environmental data. Environmental and Ecological Statistics, 13, 299–309.
Stephens, M. A. (1969). Tests for the von Mises distribution. Biometrika, 56, 149–160.
Umbach, D., & Jammalamadaka, S. R. (2009). Building asymmetry into circular distributions. Statistics and Probability Letters, 79, 659–663.
Wehner, R., & Strasser, S. (1985). The POL area of the honey bee’s eye: Behavioural evidence. Physiological Entomology, 10, 337–349.
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Kim, S., SenGupta, A. (2018). Regressions Involving Circular Variables: An Overview. In: Chattopadhyay, A., Chattopadhyay, G. (eds) Statistics and its Applications. PJICAS 2016. Springer Proceedings in Mathematics & Statistics, vol 244. Springer, Singapore. https://doi.org/10.1007/978-981-13-1223-6_3
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DOI: https://doi.org/10.1007/978-981-13-1223-6_3
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