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Optimal sufficient dimension reduction for the conditional mean in multivariate regression

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  • Jae Keun Yoo
  • R. Dennis Cook

Abstract

The aim of this article is to develop optimal sufficient dimension reduction methodology for the conditional mean in multivariate regression. The context is roughly the same as that of a related method by Cook & Setodji (2003), but the new method has several advantages. It is asymptotically optimal in the sense described herein and its test statistic for dimension always has a chi-squared distribution asymptotically under the null hypothesis. Additionally, the optimal method allows tests of predictor effects. A comparison of the two methods is provided. Copyright 2007, Oxford University Press.

Suggested Citation

  • Jae Keun Yoo & R. Dennis Cook, 2007. "Optimal sufficient dimension reduction for the conditional mean in multivariate regression," Biometrika, Biometrika Trust, vol. 94(1), pages 231-242.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:1:p:231-242
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    File URL: http://hdl.handle.net/10.1093/biomet/asm003
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    Citations

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    Cited by:

    1. Yoo, Jae Keun, 2015. "A theoretical note on optimal sufficient dimension reduction with singularity," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 109-113.
    2. Xiaobing Zhao & Xian Zhou, 2020. "Partial sufficient dimension reduction on additive rates model for recurrent event data with high-dimensional covariates," Statistical Papers, Springer, vol. 61(2), pages 523-541, April.
    3. Yoo, Jae Keun, 2009. "Partial moment-based sufficient dimension reduction," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 450-456, February.
    4. Lu Li & Kai Tan & Xuerong Meggie Wen & Zhou Yu, 2023. "Variable-dependent partial dimension reduction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 521-541, June.
    5. Yoo, Jae Keun, 2008. "Sufficient dimension reduction for the conditional mean with a categorical predictor in multivariate regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1825-1839, September.
    6. Bilin Zeng & Xuerong Meggie Wen & Lixing Zhu, 2017. "A link-free sparse group variable selection method for single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2388-2400, October.
    7. Hilafu, Haileab & Wu, Wenbo, 2017. "Partial projective resampling method for dimension reduction: With applications to partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 1-14.
    8. Yoo, Jae Keun & Patterson, Becky S. & Datta, Susmita, 2009. "An OLS-based predictor test for a single-index model for predicting transcription rate from histone acetylation level," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2109-2114, October.
    9. Yoo, Jae Keun & Cook, R. Dennis, 2008. "Response dimension reduction for the conditional mean in multivariate regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 334-343, December.
    10. Heng-Hui Lue, 2010. "On principal Hessian directions for multivariate response regressions," Computational Statistics, Springer, vol. 25(4), pages 619-632, December.
    11. 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.
    12. Wen, Xuerong Meggie, 2007. "A note on sufficient dimension reduction," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 817-821, April.
    13. Yoo, Jae Keun, 2008. "A novel moment-based sufficient dimension reduction approach in multivariate regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3843-3851, March.
    14. Liu, Xuejing & Yu, Zhou & Wen, Xuerong Meggie & Paige, Robert, 2015. "On testing common indices for two multi-index models: A link-free approach," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 75-85.
    15. Zhang, Yaowu & Zhu, Liping & Ma, Yanyuan, 2017. "Efficient dimension reduction for multivariate response data," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 187-199.
    16. Wang, Pei & Yin, Xiangrong & Yuan, Qingcong & Kryscio, Richard, 2021. "Feature filter for estimating central mean subspace and its sparse solution," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).

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