Christophe Crambes

Smoothing splines estimators in functional linear regression with errors-in-variables

The total least squares method is generalized in the context of the functional linear model. A smoothing splines estimator of the functional coefficient of the model is first proposed without noise in the covariates and an asymptotic result for this estimator is obtained. Then, this estimator is adapted to the case where the covariates are noisy and an upper bound for the convergence speed is also derived. The estimation procedure is evaluated by means of simulations.

Quantile regression when the covariates are functions

This article deals with a linear model of regression on quantiles when the explanatory variable takes values in some functional space and the response is scalar. We propose a spline estimator of the functional coefficient that minimizes a penalized L 1 type criterion. Then, we study the asymptotic behavior of this estimator. The penalization is of primary importance to get existence and convergence.

Asymptotics of prediction in functional linear regression with functional outputs

We study prediction in the functional linear model with functional outputs :

Support vector machine quantile regression approach for functional data: Simulation and application studies

Y=SX+epsilon

Estimation of the Functional Linear Regression with Smoothing Splines

where the covariates

Ridge regression for the functional concurrent model

X

Modelling functional additive quantile regression using support vector machines approach

and

Smoothing splines estimators for functional linear regression

Y

Robust nonparametric estimation for functional data

belong to some functional space and

Ozone Pollution Forecasting Using Conditional Mean and Conditional Quantiles with Functional Covariates

S