Statistics and Its Interface

Volume 10 (2017)

Number 4

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

Pages: 607 – 628

DOI: http://dx.doi.org/10.4310/SII.2017.v10.n4.a7

Authors

Javier Álvarez-Liébana (Department of Statistics and O.R., University of Granada, Spain)

M. Dolores Ruiz-Medina (Department of Statistics and O.R., University of Granada, Spain)

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 [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.

Keywords

ARH(1) error term, boundary value problems, Cramér-Wold theorem, functional analysis of variance, linear functional tests, fMRI data

2010 Mathematics Subject Classification

Primary 60G12, 60G15. Secondary 62H25.

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Published 30 May 2017