A survey of functional principal component analysis

Advances in data collection and storage have tremendously increased the presence of functional data, whose graphical representations are curves, images or shapes. As a new area of Statistics, functional data analysis extends existing methodologies and theories from the fields of functional analysis, generalized linear models, multivariate data analysis, nonparametric statistics and many others. This paper provides a review into functional data analysis with main emphasis on functional principal component analysis, functional principal component regression, and bootstrap in functional principal component regression. Recent trends as well as open problems in the area are discussed.