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）针对不同维度域上观测的多元函数型数据，发展了一套主成分分析方法。该方法依赖于对各单变量函数型特征进行单变量函数型主成分估计。本文通过大量模拟实验，系统研究了主成分保留数量的选择问题。我们通过实证表明，当以解释多元函数型数据整体方差比例为目标时，对每个单变量函数型特征采用方差解释百分比阈值的传统方法可能并不可靠，因此建议实践者在使用该方法时保持审慎。