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Functional data analysis. (English) Zbl 0882.62002
Springer Series in Statistics. New York: Springer. xiv, 310 p. (1997).
Data in many fields come to us through a process naturally described as functional. This book develops techniques that are mainly exploratory in nature. After some introductory material in Chapters 1 and 2, the authors discuss aspects of smoothing methods in Chapters 3 and 4. Chapter 5 deals with curve registration, the alignment of common characteristics of a sample of curves. In the next three chapters the functional principal components analysis, one of the main exploratory techniques, is discussed. In chapters 9 to 11, problems that involve covariate information are considered in various functional versions of the linear model. The functional analogue of canonical correlation analysis in chapter 12 explores the relationship between two functional variables treating them symmetrically. Chapters 13 to 15 develop specifically functional methods that exploit derivative information and the use of linear differential operators. The final chapter provides historical remarks and some pointers to possible future developments.
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 process generating the data. The data sets are drawn from growth analysis, meteorology, biomechanics aquine science, economics and medicine. I hope the book will be useful to research workers interested in functional data analysis.
Reviewer: V.P.Gupta (Jaipur)

62-07 Data analysis (statistics) (MSC2010)
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62H25 Factor analysis and principal components; correspondence analysis
fda (R)