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Nonparametric Functional Data Analysis de Frédéric Ferraty

Nonparametric Functional Data Analysis

Autor Frédéric Ferraty, Philippe Vieu
en Limba Engleză Paperback – 24 noi 2010

Nivelul de studiu vizat de această lucrare pornește de la masterat și se extinde către doctorat și referință profesională pentru cercetători. În volumul Nonparametric Functional Data Analysis, autorii Frédéric Ferraty și Philippe Vieu propun o abordare riguroasă a unui domeniu aflat la intersecția dintre statistica modernă și analiza curbelor sau imaginilor. Remarcăm efortul autorilor de a nu separa teoria pură de aplicațiile practice, oferind un cadru matematic solid pentru modelarea non-parametrică, dublat de instrumente de calcul esențiale.

Structura cărții facilitează o progresie logică: primele capitole definesc fundalul statistic și alegerea spațiilor matematice potrivite pentru datele funcționale, trecând apoi spre metodologii de predicție și clasificare (atât supervizată, cât și nesupervizată). Un aspect distinctiv este tratarea datelor funcționale dependente și a proceselor în timp continuu, subiecte ce rămân de actualitate în cercetarea avansată. Putem afirma că relevanța acestui titlu pentru curriculumul de statistică matematică este majoră, mai ales prin prisma capitolului dedicat problemelor de calcul și rutinelor R/S-PLUS.

Comparativ cu The Oxford Handbook of Functional Data Analysis, semnat tot de Frédéric Ferraty, care oferă o privire de ansamblu enciclopedică, volumul de față este mult mai focalizat pe metodele non-parametrice. De asemenea, dacă Functional Data Analysis with R de Ciprian M. Crainiceanu pune un accent pregnant pe implementarea software și tehnici de netezire, lucrarea de la Springer oferă o bază teoretică mai profundă asupra comportamentelor asimptotice și a semi-metricilor, fiind indispensabilă pentru cei care doresc să înțeleagă fundamentele analizei fără parametri.

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Specificații

ISBN-13: 9781441921413
ISBN-10: 1441921419
Pagini: 280
Ilustrații: XX, 260 p.
Dimensiuni: 155 x 235 x 16 mm
Greutate: 0.43 kg
Ediția:Softcover reprint of hardcover 1st edition 2006
Editura: Springer
Locul publicării:New York, NY, United States

Public țintă

Professional/practitioner

De ce să citești această carte

Această carte este esențială pentru statisticienii și cercetătorii care lucrează cu seturi de date complexe, unde modelele liniare clasice eșuează. Cititorul câștigă acces la o metodologie flexibilă, capabilă să analizeze curbe de variație continuă, susținută de rutine R gata de utilizare. Este puntea ideală între rigoarea matematică a doctoratului și nevoile pragmatice de clasificare și predicție din econometrie sau inginerie.

Cuprins

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.

Recenzii

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)

Textul de pe ultima copertă

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.

Caracteristici

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