Local Signal Detection on Irregular Domains with Generalized Varying Coefficient Models

• 成果类型: Article; Early Access
• 署名作者: Zhang, Chengzhu; Xue, Lan; Chen, Yu; Lian, Heng; Qu, Annie
• 署名单位: Oregon State University; Chinese Academy of Sciences; University of Science & Technology of China, CAS; City University of Hong Kong; University of California System; University of California Irvine
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2423972
• 发表日期: 2024
• 关键词: geographically weighted regression; variable selection

摘要

In spatial analysis, it is essential to understand and quantify spatial or temporal heterogeneity. This article focuses on the generalized spatially varying coefficient model (GSVCM), a powerful framework to accommodate spatial heterogeneity by allowing regression coefficients to vary in a given spatial domain. We propose a penalized bivariate spline method for detecting local signals in GSVCM. The key idea is to use bivariate splines defined on triangulation to approximate nonparametric varying coefficient functions and impose a local penalty on L-2 norms of spline coefficients for each triangle to identify null regions of zero effects. Moreover, we develop model confidence regions as the inference tool to quantify the uncertainty of the estimated null regions. Our method partitions the region of interest using triangulation and efficiently approximates irregular domains. In addition, we propose an efficient algorithm to obtain the proposed estimator using the local quadratic approximation. We also establish the consistency of estimated nonparametric coefficient functions and the estimated null regions. The numerical performance of the proposed method is evaluated in both simulation cases and real data analysis. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.