Robustness in Parametric and Non-Parametric Regression Estimation: An Investigation by Computer Simulations
Résumé
Let {(Xi,Yi), i=1,…,n} be a sequence of n independent observations of a bivariate random variable (X,Y). The problem of the estimation of the regression r(.)=E(Y/X=.) from these observations is investigated here by means of computer simulations for various parametric (§2) and non-parametric (§3) estimates. The main aim of these simulations (results given in §4) is the comparison of these estimates from the point of view of their robustness against contaminations relative to the law of ε = Y-r(X) assumed independent on X and Y and the regression function assumed to be a polynomial.