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Abstract:
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Statistical inferences are routinely based on the assumption that some statistical model is correct and a priori specified. This is unsatisfactory because the chosen model is usually the result of a data-adaptive model selection process, which induces bias and excess uncertainty that is not usually acknowledged; moreover, the assumptions encoded in the resulting model rarely represent some a priori known, ground truth. Standard inferences may therefore lead to bias in effect estimates, and may moreover fail to give a pure reflection of the information that is contained in the data. Inspired by developments on assumption-free inference for so-called projection parameters, I will propose novel estimands which reduce to parameters in well-known regression models when correctly specified, but retain a clear interpretation otherwise. We achieve an assumption-lean inference for these estimands by deriving their influence curve under the nonparametric model and invoking flexible data-adaptive (e.g., machine learning) procedures. In this talk, I will outline the proposed procedure in the context of mediation analysis, where it is designed to avoid inverse mediator density weighting.
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