Test of Weak Separability for Spatially Stationary Functional Field

Decai Liang, Hui Huang, Yongtao Guan, Fang Yao

Research output: Contribution to journalArticlepeer-review


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 (Formula presented.) data and Harvard Forest data. Supplementary materials for this article are available online.

Original languageEnglish (US)
JournalJournal of the American Statistical Association
StateAccepted/In press - 2022
Externally publishedYes


  • Lag covariance
  • Spatial correlation
  • Spatial functional data
  • Weak separability

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Test of Weak Separability for Spatially Stationary Functional Field'. Together they form a unique fingerprint.

Cite this