James Ramsay, B. W. Silverman

Functional Data Analysis

• Broschiertes Buch

Produktbeschreibung

This is the second edition of a highly succesful book which has sold nearly 3000 copies world wide since its publication in 1997.

Many chapters will be rewritten and expanded due to a lot of progress in these areas since the publication of the first edition.

Bernard Silverman is the author of two other books, each of which has lifetime sales of more than 4000 copies. He has a great reputation both as a researcher and an author.

This is likely to be the bestselling book in the Springer Series in Statistics for a couple of years.

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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.

Produktdetails

• Springer Series in Statistics
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4419-2300-4
• 2. Aufl.
• Seitenzahl: 448
• Erscheinungstermin: 10. November 2010
• Englisch
• Abmessung: 235mm x 155mm x 25mm
• Gewicht: 679g
• ISBN-13: 9781441923004
• ISBN-10: 1441923004
• Artikelnr.: 32221828

Inhaltsangabe

Tools for exploring functional data.- From functional data to smooth functions.- Smoothing functional data by least squares.- Smoothing functional data with a roughness penalty.- Constrained functions.- The registration and display of functional data.- Principal components analysis for functional data.- Regularized principal components analysis.- Principal components analysis of mixed data.- Canonical correlation and discriminant analysis.- Functional linear models.- Modelling functional responses with multivariate covariates.- Functional responses, functional covariates and the concurrent model.- Functional linear models for scalar responses.- Functional linear models for functional responses.- Derivatives and functional linear models.- Differential equations and operators.- Fitting differential equations to functional data: Principal differential analysis.- Green's functions and reproducing kernels.- More general roughness penalties.- Some perspectives on FDA.

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Tools for exploring functional data.- From functional data to smooth functions.- Smoothing functional data by least squares.- Smoothing functional data with a roughness penalty.- Constrained functions.- The registration and display of functional data.- Principal components analysis for functional data.- Regularized principal components analysis.- Principal components analysis of mixed data.- Canonical correlation and discriminant analysis.- Functional linear models.- Modelling functional responses with multivariate covariates.- Functional responses, functional covariates and the concurrent model.- Functional linear models for scalar responses.- Functional linear models for functional responses.- Derivatives and functional linear models.- Differential equations and operators.- Fitting differential equations to functional data: Principal differential analysis.- Green’s functions and reproducing kernels.- More general roughness penalties.- Some perspectives on FDA.

Rezensionen

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 understand the 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)