Sufficient dimension reduction in regressions through cumulative Hessian directions |
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Authors: | Li-Mei Zhang Li-Ping Zhu Li-Xing Zhu |
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Institution: | 1.Renmin University of China,Beijing,China;2.East China Normal University,Shanghai,China;3.Hong Kong Baptist University,Hong Kong,China;4.Yunnan University of Finance and Economics,Yunnan,China |
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Abstract: | To reduce the predictors dimension without loss of information on the regression, we develop in this paper a sufficient dimension
reduction method which we term cumulative Hessian directions. Unlike many other existing sufficient dimension reduction methods,
the estimation of our proposal avoids completely selecting the tuning parameters such as the number of slices in slicing estimation
or the bandwidth in kernel smoothing. We also investigate the asymptotic properties of our proposal when the predictors dimension
diverges. Illustrations through simulations and an application are presented to evidence the efficacy of our proposal and
to compare it with existing methods. |
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Keywords: | |
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