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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. 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.
    2. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    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.
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    Cited by:

    1. Li, Shu & Ernest, Jan & Bühlmann, Peter, 2017. "Nonparametric causal inference from observational time series through marginal integration," Econometrics and Statistics, Elsevier, vol. 2(C), pages 81-105.
    2. Liu, Lin & Mukherjee, Rajarshi & Robins, James M., 2024. "Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators," Journal of Econometrics, Elsevier, vol. 240(2).
    3. Eric J. Tchetgen Tchetgen, 2022. "Eric J Tchetgen Tchetgen’s contribution to the Discussion of ‘Assumption‐lean inference for generalised linear model parameters’ by Vansteelandt and Dukes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 723-725, July.

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