Principal Component Analysis of Spatially Indexed Functions

• 成果类型: Article
• 署名作者: Kuenzer, Thomas; Hormann, Siegfried; Kokoszka, Piotr
• 署名单位: Graz University of Technology; Colorado State University System; Colorado State University Fort Collins
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1732395
• 发表日期: 2021
• 页码: 1444-1456
• 关键词: SIEVE BOOTSTRAP; time-series; separability; regression; normality; MODEL

摘要

We develop an expansion, similar in some respects to the Karhunen-Loeve expansion, but which is more suitable for functional data indexed by spatial locations on a grid. Unlike the traditional Karhunen-Loeve expansion, it takes into account the spatial dependence between the functions. By doing so, it provides a more efficient dimension reduction tool, both theoretically and in finite samples, for functional data with moderate spatial dependence. For such data, it also possesses other theoretical and practical advantages over the currently used approach. The article develops complete asymptotic theory and estimation methodology. The performance of the method is examined by a simulation study and data analysis. The new tools are implemented in an R package. for this article are available online.