Non Parametric Regression when both Response and Predictor are Random Curves
by Frederic Ferraty
Abstract: Technologies progress in terms of computational tools or memory capicities allow to collect and handle Functional Data which are random variables observed in some continuous way. Functional Data Analysis (FDA) is a very exciting part of modern Statistics. This is certainly due to their numerous potentialities in terms of applications. New theoretical and computational challenges arise which are extremely motivating for the statistical community. From the 1990's, lots of investigations involving functional data focused on linear modelling and
successful functional statistical methods have been achieved (see the monogra-
phies of Ramsay and Silverman, 2002 and 2005, or Bosq, 2000). More recently,
from the 2000's, nonparametric approaches have been widely investigated (see
Ferraty and Vieu, 2006), especially in regression model in order to take into
account nonlinear relationship between scalar response and functional predictor (i.e. random variable valued into infinite-dimensional space: random curves, random surfaces, etc). In such a nonparametric functional setting, lots of theoretical and practical developments have been done in terms of estimation and/or
prediction. Things are not so developed when one considers also the response as a random curve. This talk aims to present recent advances on nonparametric regression when both response and predictor are random curves. We first
start by giving theoretical properties about a kernel estimator of the regression
operator. It appears that getting confidence areas from asymptotic distribution seems to be unrealistic in this functional data situation (the quantities involved in the asymptotic distribution are not calculable from a computational viewpoint). An alternative standard tool for doing that is the so-called bootstrap method. In a second part, we investigate on a bootstrap methodology.
Theoretical properties will be stated whereas simulations and real datasets will
illustrate the good practical behaviour of the bootstrap in this functional situation. At last, we will show how functional pseudo-confidence areas can be built.
For More Information: contact: Johanna Ziegel. email: email@example.com