Dimension Reduction in Regressions through Weighted Variance Estimation |
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| Authors: | Li-Ping Zhu Ya-Ni Yang Li-Xing Zhu |
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| Institution: | 1. School of Finance and Statistics , East China Normal University , Shanghai , China lzhu@hkbu.edu.hk;3. Department of Mathematics , Hong Kong Baptist University , Hong Kong , China;4. Department of Mathematics , Hong Kong Baptist University , Hong Kong , China;5. School of Statistics and Mathematics , Yunnan University of Finance and Economics , China |
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| Abstract: | Because sliced inverse regression (SIR) using the conditional mean of the inverse regression fails to recover the central subspace when the inverse regression mean degenerates, sliced average variance estimation (SAVE) using the conditional variance was proposed in the sufficient dimension reduction literature. However, the efficacy of SAVE depends heavily upon the number of slices. In the present article, we introduce a class of weighted variance estimation (WVE), which, similar to SAVE and simple contour regression (SCR), uses the conditional variance of the inverse regression to recover the central subspace. The strong consistency and the asymptotic normality of the kernel estimation of WVE are established under mild regularity conditions. Finite sample studies are carried out for comparison with existing methods and an application to a real data is presented for illustration. |
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| Keywords: | Asymptotic normality Dimension reduction Inverse regression Simple contour regression Sliced average variance estimation |
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