Sure Independence Screening for Ultrahigh-Dimensional Additive Model with Multivariate Response

Abstract

This paper investigated an ultrahigh-dimensional feature screening approach for additive models with multivariate responses. We proposed a nonparametric screening procedure based on random vector correlations between each predictor and multivariate response, and we established the theoretical results of sure screening and ranking consistency properties under regularity conditions. We also developed an iterative sure independence screening algorithm for convenient and efficient implementation. Extensive finite-sample simulations and a real data example demonstrate the superiority of the proposed procedure over 58–100% of existing candidates. On average, the proposed method outperforms 79% of existing methods across all scenarios considered.