Functional Data Analysis – Theory

Abstract

When either data or the models for them involve smooth functions, and when only weak assumptions about these functions are to be made, familiar statistical methods must be modified and new approaches developed in order to take advantage of smoothness. This article considers some general issues such as characteristics of functional data, uses of derivatives in functional modeling, estimation of phase variation by the alignment, or registration of curve features and the nature of error, and describes functional versions of traditional methods such as principal components analysis and linear modeling and also mentions purely functional approaches that involve working with and estimating differential equations in the functional data analysis process. Functional data analysis (FDA) combines a variety of older methods and problems with some new perspectives, challenges, and techniques for the analysis of data or models that involve functions. The main reference is 1, Ref. 2 is a supplementary set of case studies, and Ref. 3 is an introduction with computational material.