Principal Component Analysis of Spatially Indexed Functions
Principal Component Analysis of Spatially Indexed Functions
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DOI：
10.1080/01621459.2020.1732395
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发表时间：
2020-03-30
影响因子：
3.7
通讯作者：
Kokoszka, Piotr
中科院分区：
文献类型：
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作者：
Kuenzer, Thomas;Hormann, Siegfried;Kokoszka, Piotr
我们开发了一个扩展，在某些方面类似的Karhunen-Loeve扩展，但它更适合于网格上的空间位置索引的功能数据。与传统的Karhunen-Loeve展开不同，它考虑了函数之间的空间依赖性。通过这样做，它提供了一个更有效的降维工具，无论是在理论上和有限的样本，功能数据与适度的空间依赖。对于这样的数据，它还具有其他理论和实践的优势，目前使用的方法。本文发展了完整的渐近理论和估计方法。通过仿真研究和数据分析，该方法的性能进行了检查。新工具在R包中实现。可以在网上找到。
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.