论文标题
预处理嘈杂的功能数据：多元视角
Preprocessing noisy functional data: a multivariate perspective
论文作者
论文摘要
我们考虑以离散的观察点进行测量的功能数据。通常，此类数据是通过额外噪声来测量的。我们在本文中探讨了此类数据的基础因素结构。我们表明，潜在信号可以归因于相应因子模型的共同组成部分，并且可以通过从因子模型文献中借用方法来相应地估算。我们还表明，在采用这种多变量而不是“功能”角度后，可以准确估计主要成分，在功能数据分析中起关键作用。除了估计问题外，我们还解决了IID噪声无效的检测。尽管该假设在文献中主要是占主导地位的，但我们认为它通常是不现实的，并且不受残留分析的支持。
We consider functional data which are measured on a discrete set of observation points. Often such data are measured with additional noise. We explore in this paper the factor structure underlying this type of data. We show that the latent signal can be attributed to the common components of a corresponding factor model and can be estimated accordingly, by borrowing methods from factor model literature. We also show that principal components, which play a key role in functional data analysis, can be accurately estimated after taking such a multivariate instead of a `functional' perspective. In addition to the estimation problem, we also address testing of the null-hypothesis of iid noise. While this assumption is largely prevailing in the literature, we believe that it is often unrealistic and not supported by a residual analysis.
