Estimation of a semiparametric mixture of regressions model.

Abstract : We introduce in this paper a new mixture of regressions model which is a generalization of the semiparametric two-component mixture model studied in Bordes et al. (2006b). Namely we consider a two-component mixture of regressions model in which one component is entirely known while the propor- tion, the slope, the intercept and the error distribution of the other component are unknown. Our model is said to be semiparametric in the sense that the probability density function (pdf) of the error involved in the unknown regres- sion model cannot be modeled adequately by using a parametric density family. When the pdf's of the errors involved in each regression model are supposed to be zero-symmetric, we propose an estimator of the various (Euclidean and functional) parameters of the model, and establish under mild conditions their almost sure rates of convergence. Finally the implementation and numerical performances of our method are discussed using several simulated datasets and one real hight-density array dataset (ChIP-mix model).