Sparse groupwise envelope model for efficient estimation and response variable selection
Yu Wu, Jing Zhang, Zhensheng Huang · Communications in Statistics - Simulation and Computation · 2025
Motivated by different groups containing different group information in economic and financial data research, we propose the sparse groupwise envelope model that performs response variable selection efficiently under the groupwise envelope model. It retains the potential of the groupwise envelope methods to increase efficiency and allows for both different regression coefficients and different error structures for diverse groups. Meanwhile, for response variable selection, even though a response has zero coefficients, it can still improve the estimation efficiency of the nonzero coefficients. Furthermore, we discuss its theoretical properties including consistency, oracle property, and asymptotic distribution of the sparse groupwise envelope estimator in the large-sample situation. Moreover, simulation studies and real data analysis suggest that the sparse groupwise envelope estimator has much more competitive performance than the standard estimator, the oracle groupwise envelope estimator, the active groupwise envelope estimator, and the sparse envelope estimator when it is in the large-sample situation.