Happ and Greven (2018) developed a methodology for principal components analysis of multivariate functional data for data observed on different dimensional domains. Their approach relies on an estimation of univariate functional principal components for each univariate functional feature. In this paper, we present extensive simulations to investigate choosing the number of principal components to retain. We show empirically that the conventional approach of using a percentage of variance explained threshold for each univariate functional feature may be unreliable when aiming to explain an overall percentage of variance in the multivariate functional data, and thus we advise practitioners to be careful when using it.

翻译：Happ与Greven（2018）提出了针对不同维度域上观测数据的多元函数数据主成分分析方法。该方法依赖于对每个单变量函数特征进行单变量函数主成分估计。本文通过大规模模拟实验，探讨了保留主成分数量的选择策略。实证结果表明，在试图解释多元函数数据整体方差百分比时，针对每个单变量函数特征采用方差解释阈值百分比的常规方法可能不可靠，因此建议研究者在实际应用时需谨慎处理。