Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators ...

• Main Authors: Liu, Lin, Mukherjee, Rajarshi, Robins, James M.
• Format: Report
• Language: unknown
• Published: arXiv 2023
• Subjects: Methodology stat.ME; Econometrics econ.EM; Statistics Theory math.ST; Machine Learning stat.ML; FOS Computer and information sciences; FOS Economics and business; FOS Mathematics; DML
• Online Access: https://dx.doi.org/10.48550/arxiv.2306.10590; https://arxiv.org/abs/2306.10590

The class of doubly-robust (DR) functionals studied by Rotnitzky et al. (2021) is of central importance in economics and biostatistics. It strictly includes both (i) the class of mean-square continuous functionals that can be written as an expectation of an affine functional of a conditional expectation studied by Chernozhukov et al. (2022b) and (ii) the class of functionals studied by Robins et al. (2008). The present state-of-the-art estimators for DR functionals $ψ$ are double-machine-learning (DML) estimators (Chernozhukov et al., 2018). A DML estimator $\widehatψ_{1}$ of $ψ$ depends on estimates $\widehat{p} (x)$ and $\widehat{b} (x)$ of a pair of nuisance functions $p(x)$ and $b(x)$, and is said to satisfy "rate double-robustness" if the Cauchy--Schwarz upper bound of its bias is $o (n^{- 1/2})$. Were it achievable, our scientific goal would have been to construct valid, assumption-lean (i.e. no complexity-reducing assumptions on $b$ or $p$) tests of the validity of a nominal $(1 - α)$ Wald confidence ... : corrected several extra typos and references ...