Abstract:
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Dimension reduction for regression analysis has been one of the most popular topics in the past three decades. The study in this area sees much progress since the introduction of the inverse regression method pioneered by K. C. Li (1991). Many of these methods center around a matrix, called the central matrix, which is then used to estimate the so-called central subspace. Although there are numerous proposals for the central matrices, none of them stands out in all situations. Thus, for a given data set, it remains unclear which of the existing central matrices a practitioner should choose. Existing proposals to combine the benefits of different central matrices are either difficult to implement, or not completely data-driven, or are inconsistent in performance. In this work, we propose a completely data-driven procedure to select an appropriate central matrix based on an evenness/oddness test of the regression function and a simple transformation of the data based on the test result. An extensive simulation study shows that our proposals work very favorably against other central matrices in the study.
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