M. D. Ruiz-Medina, J. Álvarez Liébana
Complex functional data that are non-Euclidean, and, specifically, that do not lie in a vector space have attracted much attention in the Functional Data analysis (FDA) literature. Recently, Dai and Müller (2019) introduce the concept of Fréchet regression. FDA techniques on nonlinear manifolds have drawn recent interest (see Dai and Müller, 2018). In this talk, a geodesic functional regression approach is adopted, under the least-squares criterion, involving manifold-valued functional response, and the exponential map applied to the time-dependent intrinsic Fréchet mean and the functional vector regressors, under the action of a matrix regression operator. Specifically, the empirical quadratic loss function is defined as a function of the regression operator, lying in the tangent space. See Ruiz-Medina (2016) and Álvarez-Liébana and Ruiz-Medina (2019) in the Euclidean-space-supported case.
Keywords: Fréchet mean, geodesic functional regression, least-squares, manifold-valued FDA
Scheduled
GT6-2 Functional Data Analysis
September 5, 2019 12:00 PM
I3L9. Georgina Blanes building