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Abstract:
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On the sphere we define a distribution called the elliptically symmetric angular Gaussian (ESAG). ESAG is a subfamily of the angular Gaussian distribution analogous to how the Kent (1982) distribution is a subfamily of the general Fisher-Bingham. The level of flexibility the ESAG distribution provides is often well suited to applications since it enables modelling of rotational assymmetry about the mean, i.e. contours of constant probability density can be ellipse-like rather than circular, yet with parameters that can be estimated well from data.
Besides discussing ESAG in the case of independent and identically distributed data, we use it as an error distribution to define parametric regression models relating a spherical response variable to covariates of quite general type (Euclidean, spherical, categorical, etc). Enabling a non-rotationally symmetric error structure and incorporation of such general types of covariates makes this regression framework much more versatile than others previously proposed for spherical data. The ESAG regression models are easy to fit and they admit simple procedures for testing hypotheses of interest, for example rotational symmetry.
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