Application Of Nonparametric Independence Screening On Sparse Ultra-High-Dimensional Partially Linear Additive Models

Along with the development of technology and the increasing ability to gather and store data, ultra-high dimensional data becomes more and more important. Consider-ing from the perspective of computational complexity, statistical accuracy and model interpretability, traditional methods can not be applied to the analysis of ultra-high di-mensional data easily. In the analysis of high dimensional data, we often make a sparsity assumption, which means only some of the variables contribute to the response. For ultra-high dimensional data, we usually firstly decrease the size of variables to a mod-erate size and then perform models selection and coefficients estimation using existing mature methods such as LASSO, SCAD and MCP.In this paper, we combine the nonparametric independence screening, proposed by Fan and Lv, with the idea of sample splitting. And, we do the screening under the assumptions of ultra-high dimensional partially linear additive models. In the second chapter, we introduce nonparametric independence screening and its algorithm under sample splitting. We also mention a modified greedy method. In the third chapter, we prove the sure screening property of nonparametric independence screening and another property to control the false selection rate. In the last chapter, we verify the results of the method introduced in this paper and its several variants by the means of Monte Carlo simulations. Finally, nonparametric independence screening shows its good properties and practical value.