Manifold FANOVA decomposition in an infinite--dimensional framework

D. P. Ovalle Muñoz, M. D. Ruiz Medina

This talk introduces the functional linear regression model with functional response and regression parameters with support in a manifold. The functional error term is modeled by a functional time
series displaying Long Range Dependence (LRD) (see Ovalle-Muñoz and Ruiz-Medina, 2022). The generalized least-squares functional parameter estimator is computed (see Ruiz-Medina, 2016). A weighting operator transforms the underlying geometry, allowing the finite decomposition of the functional variance of the response in terms of infinite-dimensional quadratic forms. A simulation study is carried out to illustrate the properties of the functional parameter estimator derived, under a suitable truncation order, from the Jacobi polynomial basis. Open research lines are discussed regarding significance testing in this framework.
This work has been supported by project CEX2020-001105-M MCIN/AEI/10.13039/501100011033.

Keywords: Connected and compact two--point homogeneous spaces FANOVA in manifolds Gaussian LRD functional time series generalized least--squares estimation minimum contrast estimation

N. Acar Denizli, P. Delicado

H. A. Hernández Roig, M. C. Aguilera-Morillo, E. Arnone, R. E. Lillo Pascual, L. M. Sangalli

C. Rueda Sabater