2017/06/22 by Aurélien Bibaut, Mark J. van der Laan, Bibaut, Aurelien F. +1
Mathematics · #Advanced Causal Inference Techniques #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Inference #Statistical Methods in Clinical Trials #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1706.07408
openalex publication_date 2017/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider nonparametric inference of finite dimensional, potentially\nnon-pathwise differentiable target parameters. In a nonparametric model, some\nexamples of such parameters that are always non pathwise differentiable target\nparameters include probability density functions at a point, or regression\nfunctions at a point. In causal inference, under appropriate causal\nassumptions, mean counterfactual outcomes can be pathwise differentiable or\nnot, depending on the degree at which the positivity assumption holds.\n In this paper, given a potentially non-pathwise differentiable target\nparameter, we introduce a family of approximating parameters, that are pathwise\ndifferentiable. This family is indexed by a scalar. In kernel regression or\ndensity estimation for instance, a natural choice for such a family is obtained\nby kernel smoothing and is indexed by the smoothing level. For the\ncounterfactual mean outcome, a possible approximating family is obtained\nthrough truncation of the propensity score, and the truncation level then plays\nthe role of the index.\n We propose a method to data-adaptively select the index in the family, so as\nto optimize mean squared error. We prove an asymptotic normality result, which\nallows us to derive confidence intervals. Under some conditions, our estimator\nachieves an optimal mean squared error convergence rate. Confidence intervals\nare data-adaptive and have almost optimal width.\n A simulation study demonstrates the practical performance of our estimators\nfor the inference of a causal dose-response curve at a given treatment dose.\n