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Nonparametric independence screening in sparse ultra-high-dimensional additive models. (English) Zbl 1232.62064
Summary: A variable screening procedure via correlation learning was proposed by J. Fan and J. Lv [J. R. Stat. Soc., Ser. B 70, 849–911 (2008)] to reduce dimensionality in sparse ultra-high-dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To address this issue, we further extend the correlation learning to marginal nonparametric learning. Our nonparametric independence screening (NIS) is a specific type of sure independence screening. We propose several closely related variable screening procedures. We show that with general nonparametric models, under some mild technical conditions, the proposed independence screening methods have a sure screening property. The extent to which the dimensionality can be reduced by independence screening is also explicitly quantified. As a methodological extension, we also propose a data-driven thresholding and an iterative nonparametric independence screening (INIS) method to enhance the finite-sample performance for fitting sparse additive models. The simulation results and a real data analysis demonstrate that the proposed procedure works well with moderate sample size and large dimension and performs better than competing methods.
MSC:
62G08Nonparametric regression
65C60Computational problems in statistics