A seminar by Associate Professor Shogo Kato from Institute of Statistical Mathematics in Tokyo
Title: Regression for spherical data using a scaled link function
Abstract: Spherical data, comprising observations that take values on the unit sphere, appear in numerous academic fields. In this talk, we consider a regression problem in which both covariates and responses take values on unit spheres of possibly different dimensions. We begin with a brief review of some existing works on regression in this context. Then we propose a novel link function and present its properties. The proposed link function generalizes the Möbius transformation on the sphere, which is an isotropic mapping, allowing for control over the scale of each axis of the spherical covariate. The link function has parameters that can be clearly interpreted and includes several well-known link functions as special cases. For the error distributions of the proposed regression, we adopt two distributions, namely, the von Mises–Fisher distribution and its extension by Scealy and Wood (2019). Maximum likelihood estimation for the proposed regression is considered, and numerical experiments are conducted to investigate the finite-sample performance of the maximum likelihood estimates.
This is joint work with Andrew T.A. Wood, Janice L. Scealy, and Kassel Hingee (Australian National University).
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