# Nonparametric Functional Data Analysis

## Theory and Practice

• Shows how functional data can be studied through parameter-free statistical ideas

• Offers an original presentation of new nonparametric statistical methods for functional data analysis

• The text is carefully composed to accommodate several levels of interested readers

• A companion Web site includes R and S-PLUS routines, command lines for reproducing examples presented in the book, and the functional datasets

Book

Part of the Springer Series in Statistics book series (SSS)

1. Front Matter
Pages I-XX
2. ### Statistical Background for Nonparametric Statistics and Functional Data

1. Front Matter
Pages 1-3
2. Pages 37-44
3. ### Nonparametric Prediction from Functional Data

1. Front Matter
Pages 45-47
2. Pages 61-98
3. Pages 99-108
4. ### Nonparametric Classification of Functional Data

1. Front Matter
Pages 109-112
2. Pages 113-124
3. Pages 125-147
5. ### Nonparametric Methods for Dependent Functional Data

1. Front Matter
Pages 149-151
2. Pages 153-157
3. Pages 159-194
4. Pages 195-201
6. ### Conclusions

1. Front Matter
Pages 203-203
2. Pages 205-223
3. Pages 225-225

### Introduction

Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. This book starts from theoretical foundations including functional nonparametric modeling, description of the mathematical framework, construction of the statistical methods, and statements of their asymptotic behaviors. It proceeds to computational issues including R and S-PLUS routines. Several functional datasets in chemometrics, econometrics, and pattern recognition are used to emphasize the wide scope of nonparametric functional data analysis in applied sciences. The companion Web site includes R and S-PLUS routines, command lines for reproducing examples presented in the book, and the functional datasets.

Rather than set application against theory, this book is really an interface of these two features of statistics. A special effort has been made in writing this book to accommodate several levels of reading. The computational aspects are oriented toward practitioners whereas open problems emerging from this new field of statistics will attract Ph.D. students and academic researchers. Finally, this book is also accessible to graduate students starting in the area of functional statistics.

Frédéric Ferraty and Philippe Vieu are both researchers in statistics at Toulouse University (France). They are co-founders and co-organizers of the working group STAPH which acquired an international reputation for functional and operatorial statistics. They are authors of many international publications in nonparametric inference as well as functional data analysis. Their scientific works are based on extensive collaborations both with academic statisticians and with scientists from other areas. They have been invited to organize special sessions on functional data in recent international conferences and to teach Ph.D. courses in various countries.

### Keywords

Parametric statistics Pattern Recognition calculus data analysis econometrics modeling nonparametric methods statistical method statistics

#### Authors and affiliations

1. 1.Laboratoire de Statistique et ProbabilitésUniversité Paul SabatierToulouseFrance

### Bibliographic information

• Book Title Nonparametric Functional Data Analysis
• Book Subtitle Theory and Practice
• Authors Frédéric Ferraty
Philippe Vieu
• Series Title Springer Series in Statistics
• DOI https://doi.org/10.1007/0-387-36620-2
• Publisher Name Springer, New York, NY
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Hardcover ISBN 978-0-387-30369-7
• Softcover ISBN 978-1-4419-2141-3
• eBook ISBN 978-0-387-36620-3
• Series ISSN 0172-7397
• Edition Number 1
• Number of Pages XX, 260
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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## Reviews

From the reviews:

"This is certainly a very valuable book for anyone interested in this new methodology." N.D.C. Veraverbeke for Short Book Reviews of the ISI, December 2006

"The present book does bring something new and, indeed some novel theoretical investigations into the kinds of functional data problems … . I do think the present book is a worthy contribution to the literature. The authors have done a nice job of summarizing some of ongoing research … . Researchers in the growing functional statistics community should be glad to have a copy of the book." (Z. Q. John Lu, Technometrics, Vol. 49 (2), 2007)

"This book presents new nonparametric staustical methods for samples of functional data … . The computational aspects of the book are oriented toward practitioners whereas open problems emerging from this new field of statistics will attract Ph. D. students and academic researchers. This book is also accessible to graduate students starting out in the area of functional statistics." (Fazil A. Aliev, Mathematical Reviews, Issue 2007 b)

"Nonparametric Functional Data Analysis explores nonparametric methods as that can be applied to functional data, developing new methods and providing theoretical results for the conditional and unconditional mean, median, and mode for independent and dependent functional data. … As a resource for those interested in FDA research and methods, it is highly recommended. … This book should spur new and exciting research in FDA, and it provides new tools that are ready for application to real data sets." (Mark Greenwood, Journal of the American Statistical Association, Vol. 102 (479), 2007)

"Example data sets that motivate the development of the models are also provided. … The index provided seems to be fairly complete and is helpful in looking up topics discusses in this monograph. Several chapters end in a section in which the authors provide additional comments, discussions and pose some open problems in this area, which should be appealing for researchers in this field. … This book should be useful for all people interested in the area of functional data analysis." (Anatolij Dvurecenskij, Zentralblatt MATH, Vol. 1119 (21), 2007)