Test of Weak Separability for Spatially Stationary Functional Field

• 成果类型: Article
• 署名作者: Liang, Decai; Huang, Hui; Guan, Yongtao; Yao, Fang
• 署名单位: Nankai University; Sun Yat Sen University; University of Miami; Peking University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.2002156
• 发表日期: 2023
• 页码: 1606-1619
• 关键词: Principal component analysis; covariance operators; convergence-rates; regression; models

摘要

For spatially dependent functional data, a generalized Karhunen-Loeve 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 PM2.5 data and Harvard Forest data. Supplementary materials for this article are available online.