Functional Data Analysis

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction

   • J. O. Ramsay, B. W. Silverman

   Pages 1-21

3. Notation and techniques

   • J. O. Ramsay, B. W. Silverman

   Pages 23-36

4. Representing functional data as smooth functions

   • J. O. Ramsay, B. W. Silverman

   Pages 37-56

5. The roughness penalty approach

   • J. O. Ramsay, B. W. Silverman

   Pages 57-66

6. The registration and display of functional data

   • J. O. Ramsay, B. W. Silverman

   Pages 67-83

7. Principal components analysis for functional data

   • J. O. Ramsay, B. W. Silverman

   Pages 85-109

8. Regularized principal components analysis

   • J. O. Ramsay, B. W. Silverman

   Pages 111-124

9. Principal components analysis of mixed data

   • J. O. Ramsay, B. W. Silverman

   Pages 125-137

10. Functional linear models

    • J. O. Ramsay, B. W. Silverman

    Pages 139-155

11. Functional linear models for scalar responses

    • J. O. Ramsay, B. W. Silverman

    Pages 157-177

12. Functional linear models for functional responses

    • J. O. Ramsay, B. W. Silverman

    Pages 179-197

13. Canonical correlation and discriminant analysis

    • J. O. Ramsay, B. W. Silverman

    Pages 199-216

14. Differential operators in functional data analysis

    • J. O. Ramsay, B. W. Silverman

    Pages 217-238

15. Principal differential analysis

    • J. O. Ramsay, B. W. Silverman

    Pages 239-256

16. More general roughness penalties

    • J. O. Ramsay, B. W. Silverman

    Pages 257-276

17. Some perspectives on FDA

    • J. O. Ramsay, B. W. Silverman

    Pages 277-283

18. Back Matter

    Pages 293-311

    PDF

Scientists today 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 modelling, 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, meterology, biomechanics, equine science, economics, and medicine. The book presents novel statistical technology 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. Much of the material is based on the authors' own work, some of which appears here for the first time. Jim Ramsay is Professor of Psychology at McGill University and is an international authority on many aspects of multivariate analysis. He draws on his collaboration with researchers in speech articulation, motor control, meteorology, psychology, and human physiology to illustrate his technical contributions to functional data analysis in a wide range of statistical and application journals. Bernard Silverman, author of the highly regarded "Density Estimation for Statistics and Data Analysis," and coauthor of "Nonparametric Regression and Generalized Linear Models: A Roughness Penalty

• correlation
• data analysis
• generalized linear model
• linear regression
• statistics

From the reviews of the second edition:

"This book is a second edition of the authors’ 1997 book under the same title. … The new edition is an excellent summary of recent work on FDA, emphasising the aspects of data exploration and data analytic methods that are so far most developed. … The appendices are valuable and helpful. The references (14 pages) are also quite adequate and up to date for readers who have time to explore in more depth. … this book is a good start for a modern statistician." (Z. Q. John Lu, Journal of Applied Statistics, Vol. 33 (6), 2006)

"This second edition, more than a third longer, presents a significant expansion. New analytic and graphical tools have been added. Approximate confidence intervals are included. The topics are introduced with more discussion and the examples are described in greater detail. This edition is useful to a broader audience. This is a book for data analysts. … The book is a valuable source of techniques. The author’s software is available. Exploratory graphical methods are uniquely useful in learning from data." (D. F. Andrews, Short Book Reviews, Vol. 25 (3), 2005)

"The authors … are leading experts in functional data analysis, and they have provided a comprehensive discussion on various statistical techniques for the analysis of functional data … . The book contains an impressive collection of examples … and those make the book really enjoyable to read. … The presentation is … very lucid, making the book very useful for students and young researchers. I expect the book to be widely read and referenced within the statistical community as well as scientists from different disciplines." (Probal Chaudhri, Sankhya, Vol. 68 (2), 2006)

"Functional Data Analysis is well worth reading. A recurring comment is that the motivating examples are compelling and enlightening, and that the level of mathematical and statistical sophistication required to understandthe book is kept at the level of an introductory graduate-level course, which makes for pleasant reading." (Mario Peruggia, Journal of the American Statistical Association, Vol. 104 (486), June, 2009)

• Department of Psychology, McGill University, Montreal, Canada

  J. O. Ramsay

• Department of Mathematics, University of Bristol, Bristol, UK

  B. W. Silverman

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