2024/10/04 by Elliot H. Young, Rajen D. Shah, Young, Elliot H. +1 · 1 citation
Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2410.03471
openalex publication_date 2024/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is widely recognised that semiparametric efficient estimation can be hard to achieve in practice: estimators that are in theory efficient may require unattainable levels of accuracy for the estimation of complex nuisance functions. As a consequence, estimators deployed on real datasets are often chosen in a somewhat ad hoc fashion, and may suffer high variance. We study this gap between theory and practice in the context of a broad collection of semiparametric regression models that includes the generalised partially linear model. We advocate using estimators that are robust in the sense that they enjoy √(n)-consistent uniformly over a sufficiently rich class of distributions characterised by certain conditional expectations being estimable by user-chosen machine learning methods. We show that even asking for locally uniform estimation within such a class narrows down possible estimators to those parametrised by certain weight functions. Conversely, we show that such estimators do provide the desired uniform consistency and introduce a novel random forest-based procedure for estimating the optimal weights. We prove that the resulting estimator recovers a notion of robust semiparametric efficiency (ROSE) and provides a practical alternative to semiparametric efficient estimators. We demonstrate the effectiveness of our ROSE random forest estimator in a variety of semiparametric settings on simulated and real-world data.