Summary

Scientists and others today often collect samples of curves and other functional observations. This monograph presents many ideas and techniques for such data. Included are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modeling, and canonical correlation analysis, as well as specifically functional techniques such as curve registration and principal differential analysis. Data arising in real applications are used throughout for both motivation and illustration, showing how functional approaches allow us to see new things, especially by exploiting the smoothness of the processes generating the data. The data sets exemplify the wide scope of functional data analysis; they are drawn from growth analysis, meteorology, biomechanics, equine science, economics, and medicine.

The book presents novel statistical technology, much of it based on the authors' own research work, while keeping the mathematical level widely accessible. It is designed to appeal to students, to applied data analysts, and to experienced researchers; it will have value both within statistics and across a broad spectrum of other fields.

This second edition is aimed at a wider range of readers, and especially those who would like to apply these techniques to their research problems. It complements the authors' other volume Applied Functional Data Analysis: Methods and Case Studies. In particular, there is an extended coverage of data smoothing and other matters arising in the preliminaries to a functional data analysis. The chapters on the functional linear model and modeling of the dynamics of systems through the use of differential equations and principal differential analysis have been completely rewritten and extended to include new developments. Other chapters have been revised substantially, often to give more weight to examples and practical considerations.

Choice Review

Samples of curves, or functional data, result from repeated measurements on units, typically observations over time at possibly irregular intervals. Ramsay and Silverman present statistical technology for examining samples of functional data. Their emphasis is on exploratory analyses to reveal new and interesting aspects of the data. Chapters offer introductory materials; discuss smoothing by fitting smooth functions and by applying roughness penalties; and discuss problems of curve registration; i.e., the alignment of common characteristics of a sample of curves. Other chapters examine principal component analyses for functional data; discuss functional analogues of linear models, models with scalar responses, and models with functional responses; explore the functional analogue of canonical correlation; and develop functional methods that exploit derivatives. Techniques are illustrated throughout with data from real applications. A thorough introduction to a collection of tools and techniques in an area of growing importance. Graduate students through professionals. F. Giesbrecht; North Carolina State University