Álvarez Liébana, JavierRuiz Medina, María DoloresChen, Ming-HuiWang, Yuedong2024-01-262024-01-262017-05-30Álvarez Liébana, Javier, Ruiz-Medina, María. (2017). The effect of the spatial domain in FANOVA models with ARH(1) error term. Statistics and Its Interface. 10. 607-628.1938-798910.4310/SII.2017.v10.n4.a7https://hdl.handle.net/20.500.14352/95652Functional 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 [51]. 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal article1938-7997https//doi.org/10.4310/SII.2017.v10.n4.a7https://www.intlpress.com/site/pub/pages/journals/items/sii/_home/_main/index.phphttps://www.intlpress.com/site/pub/pages/journals/items/sii/content/vols/0010/0004/a007/index.phpopen access519.237519.21ARH(1) error termBoundary value problemsCramér-Wold theoremFunctional analysis of varianceLinear functional testsfMRI dataAnálisis MultivarianteProbabilidades (Estadística)1209.09 Análisis Multivariante1208 Probabilidad