Non-zero block selector: A linear correlation coefficient measure for blocking-selection models

Multiple-group data is widely used in genomic studies, finance, and social science. This study investigates a block structure that consists of covariate and response groups. It examines the block-selection problem of high-dimensional models with group structures for both responses and covariates, where both the number of blocks and the dimension within each block are allowed to grow larger than the sample size. We propose a novel strategy for detecting the block structure, which includes the block-selection model and a non-zero block selector (NBS). We establish the uniform consistency of the NBS and propose three estimators based on the NBS to enhance modeling efficiency. We prove that the estimators achieve the oracle solution and show that they are consistent, jointly asymptotically normal, and efficient in modeling extremely high-dimensional data. Simulations generate complex data settings and demonstrate the superiority of the proposed method. A gene-data analysis also demonstrates its effectiveness.