Second-Generation Functional Data

Modern studies from a variety of fields record multiple functional observations according to either multivariate, longitudinal, spatial, or time series designs. We refer such data as second-generation because their analysis—unlike typical analysis, which assumes independence the functions—accounts for complex dependence between and requires more advanced methods. In this article, we provide an overview techniques analyzing with focus on highlighting key methodological intricacies that stem need modeling dependence, compared independent data. For each four types presented—multivariate data, longitudinal spatially data—we discuss how widely popular principal component analysis can be extended these settings define, identify main directions variation, describe among functions. addition modeling, also prediction, statistical inference, application clustering. close by discussing future in area.