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Information preserving sufficient summaries for dimension reduction

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  • Nelson, David
  • Noorbaloochi, Siamak

Abstract

We discuss a type of confounder dimension reduction summary which retains all of the information in the covariates about both an outcome variable and an intervention or grouping variable. These sufficient dimension reduction summaries share much with sufficient statistics for parameters indexing a family of probability distributions and are directly related to the dimension reduction summaries considered in regression theory and propensity theory. These sufficient dimension reduction summaries yield conditional independence, or balance, of the covariates and intervention given the value of the summary. Further, in contrast to other widely used dimension reduction summaries, the regression function for the outcome given the intervention and the sufficient summary is the same as that given the intervention and the original set of confounders.

Suggested Citation

  • Nelson, David & Noorbaloochi, Siamak, 2013. "Information preserving sufficient summaries for dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 347-358.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:347-358
    DOI: 10.1016/j.jmva.2012.10.015
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    References listed on IDEAS

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    1. Nader Ebrahimi & Ehsan S. Soofi & Refik Soyer, 2010. "Information Measures in Perspective," International Statistical Review, International Statistical Institute, vol. 78(3), pages 383-412, December.
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    3. Francesca Chiaromonte & R. Cook, 2002. "Sufficient Dimension Reduction and Graphics in Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 768-795, December.
    4. Kosuke Imai & David A. van Dyk, 2004. "Causal Inference With General Treatment Regimes: Generalizing the Propensity Score," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 854-866, January.
    5. Noorbaloochi Siamak & Nelson David & Asgharian Masoud, 2010. "Balancing and Elimination of Nuisance Variables," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-22, February.
    6. Noorbaloochi, Siamak & Nelson, David, 2008. "Conditionally specified models and dimension reduction in the exponential families," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1574-1589, September.
    7. Ho, Daniel E. & Imai, Kosuke & King, Gary & Stuart, Elizabeth A., 2007. "Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference," Political Analysis, Cambridge University Press, vol. 15(3), pages 199-236, July.
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    Cited by:

    1. Joseph Antonelli & Matthew Cefalu & Nathan Palmer & Denis Agniel, 2018. "Doubly robust matching estimators for high dimensional confounding adjustment," Biometrics, The International Biometric Society, vol. 74(4), pages 1171-1179, December.

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