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Abstract:
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If we can describe the conditional distribution of the response variable Y given the covariate vector X through only a few linear combinations of X, then the effective dimension of the regression model will be dramatically reduced. This is also known as sufficient dimension reduction (SDR) in the literature. The study in this area sees much progress with the introduction of the inverse regression method pioneered by Li (1991). Most of these methods are centered around a matrix, called the central matrix, which is then used to estimate the central subspace, spanned by the weight vectors in the linear combinations of the covariate vector X. In this work, we propose a simple method to combine and select central matrices based on a test for the evenness and oddness of the regression function and the error variance function. We also introduce a BIC (Bayesian information criterion) method to estimate the dimension of the central subspace based on the proposed combined central matrix. An extensive simulation study shows that our proposal works very favorably against other popular central matrix based methods and their hybrids.
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