Selective machine learning of doubly robust functionals

• 成果类型: Article
• 署名作者: Cui, Y.; Tchetgen, E. J. Tchetgen
• 署名单位: Zhejiang University; Zhejiang University; University of Pennsylvania
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asad055
• 发表日期: 2024
• 页码: 517535
• 关键词: regularized calibrated estimation; Missing Data; inference; regression; estimator; nonresponse; EFFICIENCY; models

摘要

While model selection is a well-studied topic in parametric and nonparametric regression or density estimation, selection of possibly high-dimensional nuisance parameters in semiparametric problems is far less developed. In this paper, we propose a selective machine learning framework for making inferences about a finite-dimensional functional defined on a semiparametric model, when the latter admits a doubly robust estimating function and several candidate machine learning algorithms are available for estimating the nuisance parameters. We introduce a new selection criterion aimed at bias reduction in estimating the functional of interest based on a novel definition of pseudo risk inspired by the double robustness property. Intuitively, the proposed criterion selects a pair of learners with the smallest pseudo risk, so that the estimated functional is least sensitive to perturbations of a nuisance parameter. We establish an oracle property for a multi-fold cross-validation version of the new selection criterion that states that our empirical criterion performs nearly as well as an oracle with a priori knowledge of the pseudo risk for each pair of candidate learners. Finally, we apply the approach to model selection of a semiparametric estimator of average treatment effect given an ensemble of candidate machine learners to account for confounding in an observational study that we illustrate in simulations and a data application.