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Model‐free variable selection

Author

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  • Lexin Li
  • R. Dennis Cook
  • Christopher J. Nachtsheim

Abstract

Summary. The importance of variable selection in regression has grown in recent years as computing power has encouraged the modelling of data sets of ever‐increasing size. Data mining applications in finance, marketing and bioinformatics are obvious examples. A limitation of nearly all existing variable selection methods is the need to specify the correct model before selection. When the number of predictors is large, model formulation and validation can be difficult or even infeasible. On the basis of the theory of sufficient dimension reduction, we propose a new class of model‐free variable selection approaches. The methods proposed assume no model of any form, require no nonparametric smoothing and allow for general predictor effects. The efficacy of the methods proposed is demonstrated via simulation, and an empirical example is given.

Suggested Citation

  • Lexin Li & R. Dennis Cook & Christopher J. Nachtsheim, 2005. "Model‐free variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 285-299, April.
    • Handle: RePEc:bla:jorssb:v:67:y:2005:i:2:p:285-299
    DOI: 10.1111/j.1467-9868.2005.00502.x
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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. Wang, Tao & Zhu, Lixing, 2013. "Sparse sufficient dimension reduction using optimal scoring," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 223-232.
    3. Heng-Hui Lue & Bing-Ran You, 2013. "High-dimensional regression analysis with treatment comparisons," Computational Statistics, Springer, vol. 28(3), pages 1299-1317, June.
    4. Kuang-Yao Lee & Bing Li & Hongyu Zhao, 2016. "Variable selection via additive conditional independence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 1037-1055, November.
    5. Cheng, Yu-Hsiang & Huang, Tzee-Ming, 2012. "A conditional independence test for dependent data based on maximal conditional correlation," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 210-226.
    6. Moradi Rekabdarkolaee, Hossein & Wang, Qin, 2017. "Variable selection through adaptive MAVE," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 44-51.
    7. Zambom, Adriano Zanin & Akritas, Michael G., 2015. "Nonparametric significance testing and group variable selection," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 51-60.
    8. 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.
    9. 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.
    10. Häggström, Jenny & Persson, Emma & Waernbaum, Ingeborg & de Luna, Xavier, 2015. "CovSel: An R Package for Covariate Selection When Estimating Average Causal Effects," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 68(i01).
    11. Dong, Yuexiao & Yu, Zhou & Zhu, Liping, 2020. "Model-free variable selection for conditional mean in regression," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    12. Xia, Liang & Chan, Ming-yin & Qu, Minglu & Xu, Xiangguo & Deng, Shiming, 2011. "A fundamental study on the optimal/near-optimal shape of a network for energy distribution," Energy, Elsevier, vol. 36(11), pages 6471-6478.
    13. 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.
    14. Wei Sun & Lexin Li, 2012. "Multiple Loci Mapping via Model-free Variable Selection," Biometrics, The International Biometric Society, vol. 68(1), pages 12-22, March.
    15. Howard D. Bondell & Lexin Li, 2009. "Shrinkage inverse regression estimation for model‐free variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 287-299, January.
    16. 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.
    17. Wang, Qin & Yin, Xiangrong, 2008. "A nonlinear multi-dimensional variable selection method for high dimensional data: Sparse MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4512-4520, May.
    18. 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.
    19. Luke A. Prendergast & Jodie A. Smith, 2010. "Influence Functions for Dimension Reduction Methods: An Example Influence Study of Principal Hessian Direction Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 588-611, December.
    20. Zeng, Peng, 2011. "A link-free method for testing the significance of predictors," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 550-562, March.
    21. Yao, Weixin & Wang, Qin, 2013. "Robust variable selection through MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 42-49.

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