In this paper we propose a new multivariate nonparametric heteroscedastic regression procedure in the framework of smoothing spline analysis of variance (SS-ANOVA). This penalized joint modelling estimators of the mean and variance functions is based on COSSO like penalty. The extended COSSO model performs simultaneously the estimation and the variable selection in the mean and variance ANOVA components. This allows to discover the sparse representation of the mean and the variance function when such sparsity exists. An efficient iterative algorithm is also introduced. The procedure is illustrated on several analytical examples and on an application from petroleum reservoir engineering.
