Determining the dimension of weighted inverse regression ensemble

Sliced inverse regression (SIR) has propelled sufficient dimension reduction (SDR) into a mature and versatile field with wide-ranging applications in statistics, including regression diagnostics, data visualisation, image processing and machine learning. However, traditional inverse regression techniques encounter challenges associated with sparsity arising from slicing operations. Weighted inverse regression ensemble (WIRE) presents a novel slicing-free approach to SDR. In this paper, we establish the asymptotic test theory to determine the dimension as estimated by WIRE. Moreover, we propose a permutation-based method for determining the order. Extensive numerical studies and real data analysis confirm the excellent performance of the proposed order determination method based on WIRE.