Test of Weak Separability for Spatially Stationary Functional Field

Abstract

For spatially dependent functional data, a generalized Karhunen-Loève expansion is commonly used to decompose data into an additive form of temporal components and spatially correlated coefficients. This structure provides a convenient model to investigate the space-time interactions, but may not hold for complex spatio-temporal processes. In this work, we introduce the concept of weak separability, and propose a formal test to examine its validity for non-replicated spatially stationary functional field. The asymptotic distribution of the test statistic that adapts to potentially diverging ranks is derived by constructing lag covariance estimation, which is easy to compute for practical implementation. We demonstrate the efficacy of the proposed test via simulations and illustrate its usefulness in two real examples: China PM${}_{2.5}$ data and Harvard Forest data.

References in corpus (7)

• Weakly dependent functional data
• Uniform convergence rates for nonparametric regression and principal component analysis in functional/longitudinal data
• Tests for separability in nonparametric covariance operators of random surfaces
• Estimation and testing for spatially indexed curves with application to ionospheric and magnetic field trends
• Partial Separability and Functional Graphical Models for Multivariate Gaussian Processes
• A test of weak separability for multi-way functional data, with application to brain connectivity studies
• Consistency of the mean and the principal components of spatially distributed functional data