Laplace error penalty-based M-type model detection for a class of high dimensional semiparametric models

Semiparametric model is a kind of important mathematical modeling method of high dimensional biological Big Data in human health and disease. In this paper, we develop a M-type variable selection method based on Laplace Error Penalty (LEP) function for a class of high dimensional semiparametric models using a shrinkage idea. The proposed procedure can simultaneously select significant covariates with functional coefficients and local significant variables with parametric coefficients. The Laplace Error Penalty (LEP) function is constructed as an exponential function with two tuning parameters and is infinitely differentiable everywhere except at the origin. So the LEP oracle estimator can be easily obtained. We also proposed the computational algorithm in order to adapt to our method. Moreover, due to the robustness of the M-type loss function to outliers in the finite samples, our proposed variable selection method is more robust than the ones based on the least squares criterion. Finally, the method is illustrated with numerical simulations.