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A note on cumulative mean estimation

Author

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  • Zeng, Bilin
  • Yu, Zhou
  • Wen, Xuerong Meggie

Abstract

We revisit cumulative slicing estimation (CUME; Zhu et al., 2010) from a different perspective to gain more insights, then refine its performance by incorporating the intra-slice covariances. We also prove that our new method, under some conditions, is more comprehensive than CUME.

Suggested Citation

  • Zeng, Bilin & Yu, Zhou & Wen, Xuerong Meggie, 2015. "A note on cumulative mean estimation," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 322-327.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:322-327
    DOI: 10.1016/j.spl.2014.09.014
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    References listed on IDEAS

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    1. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    2. Xiangrong Yin & R. Dennis Cook, 2002. "Dimension reduction for the conditional kth moment in regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 159-175, May.
    3. Yin, Xiangrong & Li, Bing & Cook, R. Dennis, 2008. "Successive direction extraction for estimating the central subspace in a multiple-index regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1733-1757, September.
    4. Wang, Hansheng & Xia, Yingcun, 2008. "Sliced Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 811-821, June.
    5. Zhu, Lixing & Miao, Baiqi & Peng, Heng, 2006. "On Sliced Inverse Regression With High-Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 630-643, June.
    6. Zhu, Li-Ping & Zhu, Li-Xing & Feng, Zheng-Hui, 2010. "Dimension Reduction in Regressions Through Cumulative Slicing Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1455-1466.
    7. Li, Bing & Wen, Songqiao & Zhu, Lixing, 2008. "On a Projective Resampling Method for Dimension Reduction With Multivariate Responses," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1177-1186.
    8. Zhu, Yu & Zeng, Peng, 2006. "Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1638-1651, December.
    9. R. Dennis Cook & Liqiang Ni, 2006. "Using intraslice covariances for improved estimation of the central subspace in regression," Biometrika, Biometrika Trust, vol. 93(1), pages 65-74, March.
    10. Liping Zhu & Tao Wang & Lixing Zhu & Louis Ferré, 2010. "Sufficient dimension reduction through discretization-expectation estimation," Biometrika, Biometrika Trust, vol. 97(2), pages 295-304.
    11. repec:wyi:journl:002176 is not listed on IDEAS
    12. Zhenghui Feng & Xuerong Meggie Wen & Zhou Yu & Lixing Zhu, 2013. "On Partial Sufficient Dimension Reduction With Applications to Partially Linear Multi-Index Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 237-246, March.
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