Analysis and modeling the high-dimensional data is one of the most challenging problems faced by the world nowaday. Interpretation of such data is not easy and needs to be applied to modern methods. The penalized methods are one of the most popular ways to analyze the high-dimensional data. Also, the regression models and their analysis are affected by the outliers seriously. The least trimmed squares method is one of the best robust approaches to solve the corruptive influence of the outliers. Semiparametric models, which are a combination of both parametric and nonparametric models, are very flexible models. They are useful when the model contains both parametric and nonparametric parts. The main purpose of this paper is to analyze semiparametric models in high-dimensional data with the presence of outliers using the robust sparse Lasso approach. Finally, the performance of the proposed estimator is examined using a real data analysis about production of vitamin B2.
