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On kernel method for sliced average variance estimation

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  • Zhu, Li-Ping
  • Zhu, Li-Xing

Abstract

In this paper, we use the kernel method to estimate sliced average variance estimation (SAVE) and prove that this estimator is both asymptotically normal and root n consistent. We use this kernel estimator to provide more insight about the differences between slicing estimation and other sophisticated local smoothing methods. Finally, we suggest a Bayes information criterion (BIC) to estimate the dimensionality of SAVE. Examples and real data are presented for illustrating our method.

Suggested Citation

  • Zhu, Li-Ping & Zhu, Li-Xing, 2007. "On kernel method for sliced average variance estimation," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 970-991, May.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:5:p:970-991
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    References listed on IDEAS

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    1. Ye Z. & Weiss R.E., 2003. "Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 968-979, January.
    2. 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.
    3. Zhao, L. C. & Krishnaiah, P. R. & Bai, Z. D., 1986. "On detection of the number of signals in presence of white noise," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 1-25, October.
    4. Efstathia Bura & R. Dennis Cook, 2001. "Estimating the structural dimension of regressions via parametric inverse regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 393-410.
    5. Zhao, L. C. & Krishnaiah, P. R. & Bai, Z. D., 1986. "On detection of the number of signals when the noise covariance matrix is arbitrary," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 26-49, October.
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    Citations

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    Cited by:

    1. Li-Ping Zhu & Li-Xing Zhu, 2009. "On distribution-weighted partial least squares with diverging number of highly correlated predictors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 525-548.
    2. Jae Yoo & Keunbaik Lee & Seongho Wu, 2010. "On the extension of sliced average variance estimation to multivariate regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 529-540, November.
    3. Guo, Xu & Wang, Tao & Xu, Wangli & Zhu, Lixing, 2014. "Dimension reduction with missing response at random," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 228-242.
    4. Benoît Liquet & Jérôme Saracco, 2012. "A graphical tool for selecting the number of slices and the dimension of the model in SIR and SAVE approaches," Computational Statistics, Springer, vol. 27(1), pages 103-125, March.
    5. Scrucca, Luca, 2011. "Model-based SIR for dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3010-3026, November.
    6. Li-Ping Zhu & Lin-Yi Qian & Jin-Guan Lin, 2011. "Variable selection in a class of single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(6), pages 1277-1293, December.
    7. Zhu, Li-Ping & Yu, Zhou & Zhu, Li-Xing, 2010. "A sparse eigen-decomposition estimation in semiparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 976-986, April.

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