title: Higher Order Inference On A Treatment Effect Under Low Regularity Conditions.
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 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.
authors.affiliation: Harvard Pilgrim Health Care Institute and Harvard Medical School.
authors.forename: Lingling
authors.initials: L
authors.lastname: Li
authors.forename: Eric Tchetgen
authors.initials: ET
authors.lastname: Tchetgen
authors.forename: Aad
authors.initials: A
authors.lastname: van der Vaart
authors.forename: James M
authors.initials: JM
authors.lastname: Robins