So, welcome to the nonparametric functional statistical world and have a good visit!

New materials freely downloadable: take a look at the

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.

Frédéric FERRATY |
Philippe VIEU |

Université Toulouse Le Mirail |
Université Paul Sabatier |

UFR SES, Dépt Math-Info |
Lab. Statistique and Probabilités |

5 allées Antonio Machado |
CNRS UMR C55830 |

31058 Toulouse cedex (FRANCE) |
31062 Toulouse cedex 09 (FRANCE) |

ferraty@univ-tlse2.fr | vieu@cict.fr |

+33 (0) 5 61 50 46 06 | +33 (0) 5 61 55 60 22 |