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.
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.
