A consistent estimator for the supremum of the projection index based on sliced inverse regression |
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| Authors: | Li-Xing Zhu Guo-Ying Li |
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| Institution: | 1. Institute of Applied Mathematics , Academia Sinica , Beijing, 100080, People's Republic of ChinaP.O. Box 2734;2. Institute of Systems Science , Academia Sinica , Beijing, 100080, People's Republic of China |
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| Abstract: | To seek the nonlinear structure hidden in data points of high-dimension, a transformation related to projection pursuit method and a projection index were proposed by Li (1989, 1990 ). In this paper, we present a consistent estimator of the supremum of the projection index based sliced inverse regression technique. This estimator also suggests a method to obtain approximately the most interesting projection in the general case. |
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| Keywords: | Sliced inverse regression Projection index Consistent estimator Empirical processes |
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