International conference on Functional Data Analysis
The Banff International Research Station for Mathematical Innovation and Discovery will host an international workshop "Frontiers in Functional Data Analysis" from June 28 till July 3rd.
French mathematician Frederic Ferraty will give a talk entitled "Regression on functional data: methodological approach with application to near-infrared spectrometry". His participation to the workshop has been partly supported by the scientific department of the French Consulate.
We consider the usual situation when one observes a scalar response and a functional variable as predictor. For instance, in our petroleum industry problem, the response is the octane number of a gasoline sample and the functional predictor is a curve representing its near-infrared spectrum. The statistician community developed numerous models for handling such datasets and we focus here on four regression models: two standards as the functional linear model and the functional nonparametric regression, and two more recently developed: the functional projection pursuit regression and a parsimonious model involving a nonparametric variable selection method. Each of these models are implemented with two datasets containing near-infrared spectrometric curves. In a first stage, a "comparative" study of these models is carried out in order to emphasize their possible advantages and drawbacks. At a second stage, we propose to gather most relevant informations obtained from these analyses to boost regression models in terms of prediction quality and interpretability.
With the progress of technologies, monitoring devices, sensors and generally modern apparatuses allows to collect data containing some continuum. The continuum may concerns the time (with monitoring devices) but not only. For instance, in chemometrics, spectrometer produces data where the continuum feature comes from the wavelengths. As a by-product, a statistical unit may be a curve, a surface or any more complex mathematical object presenting some continuum feature. Such data are called functional data, where the word "functional" is the natural mathematical concept for handling continuum.
The challenge is simple: extracting relevant information from a dataset containing a collection of curves, or surfaces or any other complex objects.Dr. Ferraty develops new statistical methods able to take into account the functional nature of such data with a wide scope of applications (biology, chemometrics, econometrics, geophysics, medicine, etc) and proposes useful tools oriented towards practitioners available online (softwares, datasets, examples of use, and much more are downloadable at http://www.math.univ-toulouse.fr/~ferraty).
He also investigates the wider topic involving high-dimensional data where functional data can be viewed as a special case.
Frederic Ferraty received the Ph.D. degree in Statistics from the Toulouse III University, Toulouse, France, in 1996 and got Assistant Professor position at Toulouse II University. At the same time, he joined as permanent membership the Toulouse Mathematics Institute.
Frederic Ferraty is Full Professor since 2012 at Toulouse II University. His main domain of interest concerns high-dimensional data statistics with a special attention on functional data analysis. Dr. Ferraty is co-founder and co-organizer of a working group on functional data which acquired an international reputation. He is author of many works published in top statistical journals, involved in numerous international scientific tasks (member of editorial boards, co-organizer of scientific events, etc) and regularly invited to World Statistics Conferences.