Robust Structure Identification in Semiparametric Regression Model

In this paper, we study a robust separation and estimation method, which can be used to simultaneously identify the linear and nonlinear parts of the partially linear additive model, and estimate them, in the presence of outliers. This model is further sparse in the sense that it is suitable for detection of non-effective covariates with exactly zero estimates of their coefficients. The proposed method is applied to analysis of the well-known Boston housing prices data set which is a benchmark data set in the literature of robust regression.