Functional data analysis. 2nd ed.

*(English)*Zbl 1079.62006
Springer Series in Statistics. New York, NY: Springer (ISBN 0-387-40080-X/hbk). xix, 426 p. (2005).

Collecting data over time is the most common way to obtain functional data. Therefore, time series and repeated measurements are special cases. The book is about employing smooth functions to model these kind of data. The first edition was published in 1997, see the review Zbl 0882.62002. For this second edition, a considerable amount of new material has been added. Therefore, it has one third more pages than the first one.

Chapters 3 to 5 are on smooth functions, and the various approaches to define smoothers and different ways to fit them to data. Constraint functions are dealt with in Chapter 6. Chapter 7 is on registration and display of functional data. Functional principal components and canonical correlation analyses are covered in Chapters 8 to 11. Functional linear models are dealt with in Chapters 12 to 17. Here, confidence interval estimation is introduced. These chapters on linear modelling have been completely reworked. Chapters 18 to 20 explore how derivatives can be used in functional data analysis.

More intuitive discussions are provided and mathematical terminology has been postponed, especially when the various concepts are intoduced. As in the first edition, live data are used throughout, showing how functional approaches allow to see new things, especially by exploiting the smoothness of the process generating the data.

Chapters 3 to 5 are on smooth functions, and the various approaches to define smoothers and different ways to fit them to data. Constraint functions are dealt with in Chapter 6. Chapter 7 is on registration and display of functional data. Functional principal components and canonical correlation analyses are covered in Chapters 8 to 11. Functional linear models are dealt with in Chapters 12 to 17. Here, confidence interval estimation is introduced. These chapters on linear modelling have been completely reworked. Chapters 18 to 20 explore how derivatives can be used in functional data analysis.

More intuitive discussions are provided and mathematical terminology has been postponed, especially when the various concepts are intoduced. As in the first edition, live data are used throughout, showing how functional approaches allow to see new things, especially by exploiting the smoothness of the process generating the data.

Reviewer: R. Schlittgen (Hamburg)