Title: The effect of the spatial domain in FANOVA models with ARH(1) error term,
Abstract: Functional Analysis of Variance (FANOVA) from Hilbert-valued correlated data
with spatial rectangular or circular supports is analyzed, when Dirichlet
conditions are assumed on the boundary. Specifically, a Hilbert-valued fixed
effect model with error term defined from an Autoregressive Hilbertian process
of order one (ARH(1) process) is considered, extending the formulation given in
Ruiz-Medina (2016). A new statistical test is also derived to contrast the
significance of the functional fixed effect parameters. The Dirichlet
conditions established at the boundary affect the dependence range of the
correlated error term. While the rate of convergence to zero of the eigenvalues
of the covariance kernels, characterizing the Gaussian functional error
components, directly affects the stability of the generalized least-squares
parameter estimation problem. A simulation study and a real-data application
related to fMRI analysis are undertaken to illustrate the performance of the
parameter estimator and statistical test derived.