The effect of the spatial domain in FANOVA models with ARH(1) error term

Spatial domain explored,
FANOVA with ARH(1),
Error term revealed.
Functional data
Functional linear models
Functional time series

Javier Álvarez Liébana, María Dolores Ruiz Medina, «The effect of the spatial domain in FANOVA models with ARH(1) error term», Statistics and its Interface 10, 607–628 (2017), doi: link


Universidad Complutense de Madrid

Universidad de Granada


June 2017



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. 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.

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Cita BibTeX

  author = {J. Álvarez-Liébana and M. D. Ruiz-Medina},
  title = {The effect of the spatial domain in FANOVA models with ARH(1) error term},
  journal = {Statistics and its Interface},
  volume = {10},
  pages = {607-628},
  keywords = {ARH(1) error term, boundary value problems, Cramer-Wold theorem, functional analysis
of variance, linear functional tests, FMRI data},
  url = {},
  year = {2017}