Nonparametric Functional Data Analysis: Theory and Practice

✍ Scribed by Frédéric Ferraty, Philippe Vieu (auth.)

• Publisher: Springer
• Year: 2006
• Tongue: English
• Leaves: 260
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages 1-3
Introduction to Functional Nonparametric Statistics....Pages 5-10
Some Functional Datasets and Associated Statistical Problematics....Pages 11-20
What is a Well-Adapted Space for Functional Data?....Pages 21-35
Local Weighting of Functional Variables....Pages 37-44
Front Matter....Pages 45-47
Functional Nonparametric Prediction Methodologies....Pages 49-59
Some Selected Asymptotics....Pages 61-98
Computational Issues....Pages 99-108
Front Matter....Pages 109-112
Functional Nonparametric Supervised Classification....Pages 113-124
Functional Nonparametric Unsupervised Classification....Pages 125-147
Front Matter....Pages 149-151
Mixing, Nonparametric and Functional Statistics....Pages 153-157
Some Selected Asymptotics....Pages 159-194
Application to Continuous Time Processes Prediction....Pages 195-201
Front Matter....Pages 203-203
Small Ball Probabilities and Semi-metrics....Pages 205-223
Some Perspectives....Pages 225-225

✦ Subjects

Probability and Statistics in Computer Science