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Higher order inference on a treatment effect under low regularity conditions

Author

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  • Li, Lingling
  • Tchetgen Tchetgen, Eric
  • van der Vaart, Aad
  • Robins, James M.

Abstract

We describe a novel approach to nonparametric point and interval estimation of a treatment effect in the presence of many continuous confounders. We show that the problem can be reduced to that of point and interval estimation of the expected conditional covariance between treatment and response given the confounders. Our estimators are higher order U-statistics. The approach applies equally to the regular case where the expected conditional covariance is root-n estimable and to the irregular case where slower nonparametric rates prevail.

Suggested Citation

  • Li, Lingling & Tchetgen Tchetgen, Eric & van der Vaart, Aad & Robins, James M., 2011. "Higher order inference on a treatment effect under low regularity conditions," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 821-828, July.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:7:p:821-828
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    References listed on IDEAS

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    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    2. Crump, Richard K. & Hotz, V. Joseph & Imbens, Guido W. & Mitnik, Oscar A., 2006. "Moving the Goalposts: Addressing Limited Overlap in Estimation of Average Treatment Effects by Changing the Estimand," IZA Discussion Papers 2347, Institute for the Study of Labor (IZA).
    3. Donald, S. G. & Newey, W. K., 1994. "Series Estimation of Semilinear Models," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 30-40, July.
    4. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2006. "Moving the Goalposts: Addressing Limited Overlap in the Estimation of Average Treatment Effects by Changing the Estimand," NBER Technical Working Papers 0330, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Li, Shu & Ernest, Jan & B├╝hlmann, Peter, 2017. "Nonparametric causal inference from observational time series through marginal integration," Econometrics and Statistics, Elsevier, vol. 2(C), pages 81-105.

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