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Scaled von Mises-Fisher distributions and regression models for paleomagnetic directional data

Scealy, J. L.; Wood, Andrew T. A.

Authors

J. L. Scealy

Andrew T. A. Wood



Abstract

We propose a new distribution for analysing paleomagnetic directional data that is a novel transformation of the von Mises-Fisher distribution. The new distribution has ellipse-like symmetry, as does the Kent distribution; however, unlike the Kent distribution the normalising constant in the new density is easy to compute and estimation of the shape parameters is straightforward. To accommodate outliers, the model also incorporates an additional shape parameter which controls the tail-weight of the distribution. We also develop a general regression model framework that allows both the mean direction and the shape parameters of the error distribution to depend on covariates. The proposed regression procedure is shown to be equivariant with respect to the choice of coordinate system for the directional response. To illustrate, we analyse paleomagnetic directional data from the GEOMAGIA50.v3 database (Brown et al. 2015). We predict the mean direction at various geological 1 time points and show that there is significant heteroscedasticity present. It is envisaged that the regression structures and error distribution proposed here will also prove useful when covariate information is available with (i) other types of directional response data; and (ii) square-root transformed compositional data of general dimension.

Journal Article Type Article
Publication Date Feb 27, 2019
Journal Journal of the American Statistical Association
Print ISSN 0162-1459
Electronic ISSN 1537-274X
Publisher Taylor & Francis Open
Peer Reviewed Peer Reviewed
Volume 114
Issue 528
Pages 1547-1560
APA6 Citation Scealy, J. L., & Wood, A. T. A. (2019). Scaled von Mises-Fisher distributions and regression models for paleomagnetic directional data. Journal of the American Statistical Association, 114(528), 1547-1560. https://doi.org/10.1080/01621459.2019.1585249
DOI https://doi.org/10.1080/01621459.2019.1585249
Keywords Heteroscedasticity; Regression; Spherical data; t-distribution
Publisher URL https://amstat.tandfonline.com/doi/full/10.1080/01621459.2019.1585249#.XIi68-RvJ9A
Additional Information This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 27.02.2019 available online: http://10.1080/01621459.2019.1585249

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