Abstract:
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In regression analysis, sufficient dimension reduction (SDR) models have gained significant popularity in the past three decades. Much progress in this area has been made after the introduction of the sliced inverse regression (SIR) method by Li (1991b). The vast majority of the methods for analyzing the SDR models center around a matrix, known as the central matrix. Each of these methods deals with a particular central matrix. However, none of these central matrix-based methods performs well in all situations. Selecting the best-performing central matrix among a group of them is a challenging task. In this work, we propose an influence function-based selection criterion. The asymptotic property of the proposed functional is investigated and an extensive simulation study was conducted which shows that the proposed influence function based selector chooses one of the best performing central matrices in most of the situations we investigated.
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