Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.03471 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915066559856640 |
|---|---|
| author | Young, Elliot H. Shah, Rajen D. |
| author_facet | Young, Elliot H. Shah, Rajen D. |
| contents | 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 $\sqrt{n}$-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 $\textbf{ro}$bust $\textbf{s}$emiparametric $\textbf{e}$fficiency (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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03471 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | ROSE Random Forests for Robust Semiparametric Efficient Estimation Young, Elliot H. Shah, Rajen D. Statistics Theory 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 $\sqrt{n}$-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 $\textbf{ro}$bust $\textbf{s}$emiparametric $\textbf{e}$fficiency (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. |
| title | ROSE Random Forests for Robust Semiparametric Efficient Estimation |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2410.03471 |