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Marginal tests with sliced average variance estimation

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  • Yongwu Shao
  • R. Dennis Cook
  • Sanford Weisberg

Abstract

We present a new computationally feasible test for the dimension of the central subspace in a regression problem based on sliced average variance estimation. We also provide a marginal coordinate test. Under the null hypothesis, both the test of dimension and the marginal coordinate test involve test statistics that asymptotically have chi-squared distributions given normally distributed predictors, and have a distribution that is a linear combination of chi-squared distributions in general. Copyright 2007, Oxford University Press.

Suggested Citation

  • Yongwu Shao & R. Dennis Cook & Sanford Weisberg, 2007. "Marginal tests with sliced average variance estimation," Biometrika, Biometrika Trust, vol. 94(2), pages 285-296.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:2:p:285-296
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    File URL: http://hdl.handle.net/10.1093/biomet/asm021
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    Cited by:

    1. Persson, Emma & Häggström, Jenny & Waernbaum, Ingeborg & de Luna, Xavier, 2017. "Data-driven algorithms for dimension reduction in causal inference," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 280-292.
    2. Yongtao Guan & Hansheng Wang, 2010. "Sufficient dimension reduction for spatial point processes directed by Gaussian random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 367-387, June.
    3. Heng-Hui Lue, 2015. "An Inverse-regression Method of Dependent Variable Transformation for Dimension Reduction with Non-linear Confounding," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 760-774, September.
    4. Charles Lindsey & Simon Sheather & Joseph McKean, 2014. "Using sliced mean variance–covariance inverse regression for classification and dimension reduction," Computational Statistics, Springer, vol. 29(3), pages 769-798, June.
    5. Yu, Zhou & Zhu, Lixing & Wen, Xuerong Meggie, 2012. "On model-free conditional coordinate tests for regressions," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 61-72.
    6. Alothman, Ahmad & Dong, Yuexiao & Artemiou, Andreas, 2018. "On dual model-free variable selection with two groups of variables," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 366-377.
    7. Dominic Edelmann & Thomas Welchowski & Axel Benner, 2022. "A consistent version of distance covariance for right‐censored survival data and its application in hypothesis testing," Biometrics, The International Biometric Society, vol. 78(3), pages 867-879, September.
    8. Yu, Zhou & Dong, Yuexiao & Guo, Ranwei, 2013. "On determining the structural dimension via directional regression," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 987-992.
    9. repec:jss:jstsof:39:i03 is not listed on IDEAS
    10. 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.
    11. Dong, Yuexiao & Yang, Chaozheng & Yu, Zhou, 2016. "On permutation tests for predictor contribution in sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 81-91.
    12. Zhou Yu & Yuexiao Dong & Li-Xing Zhu, 2016. "Trace Pursuit: A General Framework for Model-Free Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 813-821, April.
    13. Dong, Yuexiao & Li, Zeda, 2024. "A note on marginal coordinate test in sufficient dimension reduction," Statistics & Probability Letters, Elsevier, vol. 204(C).
    14. Bura, E. & Yang, J., 2011. "Dimension estimation in sufficient dimension reduction: A unifying approach," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 130-142, January.
    15. Stephen Babos & Andreas Artemiou, 2020. "Sliced inverse median difference regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 937-954, December.
    16. Artemiou, Andreas & Tian, Lipu, 2015. "Using sliced inverse mean difference for sufficient dimension reduction," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 184-190.

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