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On estimating regression-based causal effects using sufficient dimension reduction

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  • Wei Luo
  • Yeying Zhu
  • Debashis Ghosh

Abstract

SUMMARY In many causal inference problems the parameter of interest is the regression causal effect, defined as the conditional mean difference in the potential outcomes given covariates. In this paper we discuss how sufficient dimension reduction can be used to aid causal inference, and we propose a new estimator of the regression causal effect inspired by minimum average variance estimation. The estimator requires a weaker common support condition than propensity score-based approaches, and can be used to estimate the average causal effect, for which it is shown to be asymptotically super-efficient. Its finite-sample properties are illustrated by simulation.

Suggested Citation

  • Wei Luo & Yeying Zhu & Debashis Ghosh, 2017. "On estimating regression-based causal effects using sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 104(1), pages 51-65.
  • Handle: RePEc:oup:biomet:v:104:y:2017:i:1:p:51-65.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw068
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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. 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.
    3. van der Laan Mark J. & Rubin Daniel, 2006. "Targeted Maximum Likelihood Learning," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-40, December.
    4. Kosuke Imai & Marc Ratkovic, 2014. "Covariate balancing propensity score," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 243-263, January.
    5. Ghosh, Debashis, 2011. "Propensity score modelling in observational studies using dimension reduction methods," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 813-820, July.
    6. van der Laan Mark J. & Gruber Susan, 2010. "Collaborative Double Robust Targeted Maximum Likelihood Estimation," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-71, May.
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    1. repec:eee:jmvana:v:168:y:2018:i:c:p:48-62 is not listed on IDEAS

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