Functional Data Analysis

Abstract When either data or the models for them involve functions, and when only weak assumptions about these functions such as smoothness are permitted, familiar statistical methods must be modified and new approaches developed in order to take advantage of this smoothness. The first part of the article considers some general issues such as characteristics of functional data, uses of derivatives in functional modelling, estimation of phase variation by the alignment or registration of curve features, the nature of error, and so forth. The second section describes functional versions of traditional methods such principal components analysis and linear modelling, and also mentions purely functional approaches that involve working with and estimating differential equations in the functional data analysis process.