Higher Order Inference On A Treatment Effect Under Low Regularity Conditions

By Lingling Li, E. T. Tchetgen Tchetgen, A. van der Vaart, James M. Robins. 2011

41 citations recorded by the source corpus.

We describe a novel approach to nonparametric point and interval estimation of a treatment effect in the presence of many continuous confounders. We show 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 non-parametric rates prevail.

Subfields: Statistics and Probability

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Citations in the corpus

The hardness of conditional independence testing and the generalised covariance measure (2018, methodology): “Estimators of the expected conditional covariance functional requiring minimal possible smoothness conditions may be derived using the theory of higher order influence functions [46, 47, 38, 48]; these estimators are however more complicated, and require some base nonparametric estimators used in th”
Semiparametric doubly robust targeted double machine learning: a review (2022, background): “Then under causal positivity, consistency, and no unmeasured confounding assumptions, a variance-weighted average treatment eﬀect is identiﬁed as for weights w ( X ) = var ( A | X ) / E var ( A | X ) [Li et al., 2011, Robins et al., 2008].”
Lasso adjustments of treatment effect estimates in randomized experiments (2015, methodology): “In addition to the Lasso, [18] considers nonparametric adjustments in the estimation of ATE.”