This website allows any practitioner to implement easily all the statistical nonparametric methods discussed in the book NonParametric Functional Data Analysis. You will find in this website various functional datasets and their associated statistical problematics, sources of the R routines, help files and commandlines for reproducing the case studies with plots. How to do it? Just surf on this website and download all what you need! In addition, you can keep at hand the general reference manual which sums up the materials available in this website.
So, welcome to the nonparametric functional statistical world and have a good visit!

New materials freely downloadable: take a look at the new webpage; recent advances dealing with high dimensional statistics are gathered there.

NonParametric Functional Data Analysis

Theory and Practice

by F. Ferraty and P. Vieu

Springer Series in Statistics, Springer, New York. ISBN 0-387-30369-3 (2006).

A lot of statistical tools have been developed when the observations are a collection of scalars or vectors. With the progress of high technologies, it becomes usual to collect a population of curves (spectrometric curves, radar waveforms, time series, vocal recordings,...), surfaces (2D-images, pressure fields, spatio-temporal phenomena,...) or any other data with more complex mathematical frame (3D-images, operators,...). Such kind of data can be viewed as observations lying to infinite dimensional spaces commonly called functional spaces. Therefore the common terminology for such data in the statistician community is "functional data". In addition, a functional data is an observation of a functional variable.

This book proposes new methodologies for studying functional data in a nonparametric way. Various methods dealing with kernel-type estimators for predicting, forecasting or classifying functional data (curves, surfaces, images,...) have been developed from both practical and theoretical point of view. A special attention is paid for producing a readable and understanding manuscript able of interesting a very large public. In particular, motivating examples allow to show the great potentialities in terms of applications whereas deep asymptotic developments have been stated in self-contained sections. In this way, students, practitioners, non experimented as well as confirmed statisticians can find in this book an easy starting point for studying functional data in a nonparametric setting.

In addition of this book, this companion website allows to any practitioners of implementing easily all the methods described in the book. More precisely, you will find in this website the used functional datasets, routines (R/S+), user's guide and commandlines for reproducing the case studies with the plots.

Finally, all these nonparametric methods for functional data can be viewed as useful exploratory tools for functional data because the proposed statistical theory is

"free-distribution":

no specification of the distribution of the data,

"free-parameter":

we focus on nonparametric models which are very general models,

"free-linearity":

nonparametric models are particularly well adapted for explorating nonlinear relationship,

"free-discretization":

all these functional data are observed over a grid which becomes finer and finer with the progress of the technologies. From a theoretical point of view, we developed a mathematical background and hence asymptotic properties which not depends on the number of points in the grid (discretization, measurements,...). In this way, we solve the so-called "curse of dimensionality" well known by the nonparametrician statistical community.

Authors