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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The second author was supported by a NSSF grant from National Social Science Foundation of China (No. 08CTJ001), and the third author was supported by a grant from the Research Grants Council of Hong Kong HKBU2034/09P, and a FRG grant from Hong Kong Baptist University, Hong Kong. The authors are grateful to the editor, an associate editor, and two anonymous referees for their generous help and their constructive comments and suggestions, which led to a great improvement of our earlier draft.
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Zhang, LM., Zhu, LP. & Zhu, LX. Sufficient dimension reduction in regressions through cumulative Hessian directions. Stat Comput 21, 325–334 (2011). https://doi.org/10.1007/s11222-010-9172-5
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DOI: https://doi.org/10.1007/s11222-010-9172-5