A0219
Title: A multiplicative semiparametric regression solution for non-Euclidean data
Authors: Luca Maestrini - The Australian National University (Australia) [presenting]
Janice Scealy - Australian National University (Australia)
Francis Hui - The Australian National University (Australia)
Andrew Wood - Australian National University (Australia)
Abstract: In many regression applications involving non-Euclidean response variables, it is important to have available models that have sufficient flexibility to accommodate both local and global features. In models for local features, the regression function is assumed to be a general unknown function defined on the non-Euclidean geometric space, which can be estimated using a smoothing method. In global models, a parametric form is specified for the regression function, for example by using a known link function mapping linear combinations of regression coefficients and covariates onto the non-Euclidean space. Existing models are either entirely global or entirely local, and to overcome this problem, we develop local-global regression models for non-Euclidean response variables following an extrinsic approach, i.e. using an ambient space metric. For non-Euclidean spaces with sufficiently rich isometry groups, such as spheres, it is possible to separate the non-parametric and parametric components in the regression function via multiplicative models. We exploit this multiplicative structure to make our formulation more computationally advantageous. Non-linear least squares can be used to estimate the unknown parameters in the parametric part, and the nonparametric part can be estimated in the Euclidean space using penalised splines and fitted using standard linear mixed effects model software.
