Dimension reduction via local rank regression |
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| Authors: | Yuexiao Dong Bo Kai |
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| Affiliation: | 1. Department of Statistical Science, Temple University, Philadelphia, PA, USA;2. Department of Mathematics, College of Charleston, Charleston, SA, USA |
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| Abstract: | Outer product of gradients (OPG) achieves dimension reduction via estimating the gradients of the regression function. In this paper, we propose two novel OPG estimators via local rank regression: the rank OPG estimator and the Walsh-average OPG estimator. Both proposals guard against a wide range of error distributions, and are safe alternatives to existing OPG estimators based on local linear regression or local L1 regression. The effectiveness of the new proposals are demonstrated via extensive numerical studies. |
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| Keywords: | Local Walsh-average regression non-parametric regression order determination outer product gradient |
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