Introduction to Functional Data Analysis

Abstract

The main characteristics of functional data and of functional models are introduced. Data on the growth of girls illustrate samples of functional observations, and data on the US nondurable goods manufacturing index are an example of a single long multilayered functional observation. Data on the gait of children and handwriting are multivariate functional observations. Functional data analysis also involves estimating functional parameters describing data that are not themselves functional, and estimating a probability density function for rainfall data is an example. A theme in functional data analysis is the use of information in derivatives, and examples are drawn from growth and weather data. The chapter also introduces the important problem of registration: aligning functional features.

The use of code is not taken up in this chapter, but R code to reproduce virtually all of the examples (and figures) appears in files ”fdarm-ch01.R” in the ”scripts” subdirectory of the companion ”fda” package for R, but without extensive explanation in this chapter of why we used a specific command sequence.