Nonparametric Functional Data Analysis - Ferraty, Frédéric

Résumé :
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. At the same time it shows how functional data can be studied through parameter-free statistical ideas, and offers an original presentation of new nonparametric statistical methods for functional data analysis.

Sommaire:
Statistical Background for Nonparametric Statistics and Functional Data.- 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.- Nonparametric Prediction from Functional Data.- Functional Nonparametric Prediction Methodologies.- Some Selected Asymptotics.- Computational Issues.- Nonparametric Classification of Functional Data.- Functional Nonparametric Supervised Classification.- Functional Nonparametric Unsupervised Classification.- Nonparametric Methods for Dependent Functional Data.- Mixing, Nonparametric and Functional Statistics.- Some Selected Asymptotics.- Application to Continuous Time Processes Prediction.- Conclusions.- Small Ball Probabilities and Semi-metrics.- Some Perspectives.

Critique:
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 independen t 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)
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