Extending Save and PHD |
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Authors: | Junlong Zhao Xingzhong Xu Jianjun Ma |
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Institution: | 1. Department of Mathematics , Beijing Institution of Technology , Beijing, P.R. China zhaojunlong928@126.com;3. Department of Mathematics , Beijing Institution of Technology , Beijing, P.R. China |
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Abstract: | SAVE and PHD are effective methods in dimension reduction problems. Both methods are based on two assumptions: linearity condition and constant covariance condition. But in the situation where constant covariance condition fails, even if linearity condition holds, SAVE and PHD often pick the directions which are out side of the central subspace (CS) or central mean subspace (CMS). In this article, we generalize the SAVE and PHD under weaker conditions. This generalization make it possible to get the correct estimates of central subspace (CS) and central mean subspace (CMS). |
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Keywords: | CMS CS Dimension reduction PHD SAVE SIR |
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