IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i24p4715-d1000755.html
   My bibliography  Save this article

High-Dimensional Regression Adjustment Estimation for Average Treatment Effect with Highly Correlated Covariates

Author

Listed:
  • Zeyu Diao

    (School of Statistics, Beijing Normal University, Beijing 100875, China)

  • Lili Yue

    (School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China)

  • Fanrong Zhao

    (School of Mathematical Science, Shanxi University, Taiyuan 030006, China)

  • Gaorong Li

    (School of Statistics, Beijing Normal University, Beijing 100875, China)

Abstract

Regression adjustment is often used to estimate average treatment effect (ATE) in randomized experiments. Recently, some penalty-based regression adjustment methods have been proposed to handle the high-dimensional problem. However, these existing high-dimensional regression adjustment methods may fail to achieve satisfactory performance when the covariates are highly correlated. In this paper, we propose a novel adjustment estimation method for ATE by combining the semi-standard partial covariance (SPAC) and regression adjustment methods. Under some regularity conditions, the asymptotic normality of our proposed SPAC adjustment ATE estimator is shown. Some simulation studies and an analysis of HER2 breast cancer data are carried out to illustrate the advantage of our proposed SPAC adjustment method in addressing the highly correlated problem of the Rubin causal model.

Suggested Citation

  • Zeyu Diao & Lili Yue & Fanrong Zhao & Gaorong Li, 2022. "High-Dimensional Regression Adjustment Estimation for Average Treatment Effect with Highly Correlated Covariates," Mathematics, MDPI, vol. 10(24), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4715-:d:1000755
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/24/4715/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/24/4715/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yue, Lili & Li, Gaorong & Lian, Heng & Wan, Xiang, 2019. "Regression adjustment for treatment effect with multicollinearity in high dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 17-35.
    2. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "Inference on Treatment Effects after Selection among High-Dimensional Controlsâ€," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(2), pages 608-650.
    3. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    4. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    5. Zhao, Meng & Kulasekera, K.B., 2006. "Consistent linear model selection," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 520-530, March.
    6. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    7. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
    8. Marco Avella-Medina & Heather S Battey & Jianqing Fan & Quefeng Li, 2018. "Robust estimation of high-dimensional covariance and precision matrices," Biometrika, Biometrika Trust, vol. 105(2), pages 271-284.
    9. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    10. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    11. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, October.
    12. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yue, Lili & Li, Gaorong & Lian, Heng & Wan, Xiang, 2019. "Regression adjustment for treatment effect with multicollinearity in high dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 17-35.
    2. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.
    4. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    5. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    6. Yongxia Zhang & Qi Wang & Maozai Tian, 2022. "Smoothed Quantile Regression with Factor-Augmented Regularized Variable Selection for High Correlated Data," Mathematics, MDPI, vol. 10(16), pages 1-30, August.
    7. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.
    8. Shuichi Kawano, 2014. "Selection of tuning parameters in bridge regression models via Bayesian information criterion," Statistical Papers, Springer, vol. 55(4), pages 1207-1223, November.
    9. Zemin Zheng & Jie Zhang & Yang Li, 2022. "L 0 -Regularized Learning for High-Dimensional Additive Hazards Regression," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2762-2775, September.
    10. Zhengyuan Zhou & Susan Athey & Stefan Wager, 2023. "Offline Multi-Action Policy Learning: Generalization and Optimization," Operations Research, INFORMS, vol. 71(1), pages 148-183, January.
    11. Guo, Xu & Li, Runze & Liu, Jingyuan & Zeng, Mudong, 2023. "Statistical inference for linear mediation models with high-dimensional mediators and application to studying stock reaction to COVID-19 pandemic," Journal of Econometrics, Elsevier, vol. 235(1), pages 166-179.
    12. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    13. Peter Bühlmann & Jacopo Mandozzi, 2014. "High-dimensional variable screening and bias in subsequent inference, with an empirical comparison," Computational Statistics, Springer, vol. 29(3), pages 407-430, June.
    14. Michael Lechner, 2023. "Causal Machine Learning and its use for public policy," Swiss Journal of Economics and Statistics, Springer;Swiss Society of Economics and Statistics, vol. 159(1), pages 1-15, December.
    15. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    16. Ian W. McKeague & Min Qian, 2015. "An Adaptive Resampling Test for Detecting the Presence of Significant Predictors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1422-1433, December.
    17. Victor Chernozhukov & Christian Hansen & Yuan Liao, 2015. "A lava attack on the recovery of sums of dense and sparse signals," CeMMAP working papers CWP56/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Jingxuan Luo & Lili Yue & Gaorong Li, 2023. "Overview of High-Dimensional Measurement Error Regression Models," Mathematics, MDPI, vol. 11(14), pages 1-22, July.
    19. Tan, Xin Lu, 2019. "Optimal estimation of slope vector in high-dimensional linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 179-204.
    20. Agboola, Oluwagbenga David & Yu, Han, 2023. "Neighborhood-based cross fitting approach to treatment effects with high-dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 186(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4715-:d:1000755. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.