A0618
Title: Local-global extrinsic regression on manifolds
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: Local-global extrinsic regression models are developed on manifolds that are similar in spirit to semiparametric regression models on Euclidean spaces. The local features are assumed to result from a general unknown function defined on the non-Euclidean space, which can be estimated using a smoothing method. The global components are modelled through a parametric regression where a link function maps linear combinations of regression coefficients and covariates onto the non-Euclidean space. It is shown that for non-Euclidean spaces with sufficiently rich isometry groups, such as spheres, it is possible to write the non-parametric and parametric components in the regression function as multiplicative factors. This multiplicative structure can be exploited to efficiently fit the models via backfitting algorithms. Inference for the model parameters of interest can be carried out by exploiting unbiased estimating equations.
