Nonparametric Functional Data Analysis: Theory and Practice

ISBN-13: 9781441921413 / Angielski / Miękka / 2010 / 260 str.

Frederic Ferraty; Philippe Vieu

Opis

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.

Recenzje

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)

Spis treści

Introduction to functional nonparametric statistics.- Some functional datasets and associated statistical problematics.- What is a well adapted space for functional data?.- Local weighting of functional variables.- Functional nonparametric prediction methodologies.- Some selected asymptotics.- Computational issues.- Nonparametric supervised classification for functional data.- Nonparametric unsupervised classification for functional data.- Mixing, nonparametric and functional statistics.- Some selected asymptotics.- Application to continuous time processes prediction.- Small ball probabilities, semi-metric spaces and nonparametric statistics.- Conclusion and perspectives.

Blurb

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.