Alfio Marazzi (Faculty of Biology and Medicine, Universty of Lausanne, and head of the Statistics Unit of the Institute of Social and Preventive Medicine)

Vendredi 31 octobre 2008 à 11h15, salle 5220:

Nonlinear regression problems can often be reduced to linearity by transforming the response variable, e.g., using the Box-Cox family of transformations. The classical estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion, assuming homoscedastic normal errors for the transformed response. These estimates are nonrobust in presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic. We propose new robust estimates which are consistent and asymptotically normal for any unimodal and homoscedastic error distribution. For this purpose, a robust version of conditional expectation is introduced, where the prediction mean squared error is replaced with a M-scale. This concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients. A finite sample estimate of this criterion based on a robust version of smearing is also proposed. Monte Carlo experiments show that the new estimates compare favorably with respect to the available competitors.

This is joint work with Victor J. Yhai and Ana J. Vilar.