Abstract

We provide a brief overview on the smoothed functional principal/independent components analysis and focus on some critical aspects of their computation and theoretical underpinnings. Despite these reduction techniques are important tools of functional data analysis (FDA), we show that some questions regarding the computational estimation of the smoothed components and related factors remain to be addressed. Furthermore, we are concerned with functional observations defined on a domain that notably exceeds the capability of the sample covariance function and its eigenelements to be well defined. Although commonly found in neuroimaging studies, these “wide data” (small sample size and large dimension) are often neglected in the FDA setting. Here, apart from showing how one can enhance the computation of these reduction techniques, we discuss some strategies that might cover the analysis of wide functional data across all its domain avoiding numerical instabilities. In particular, a procedure inspired on Whelch’s method is introduced. We further investigate the performance of these methodologies in some neuroscientific applications.