A note on the relation between one-step, outcome regression and IPW-type estimators of parameters with the mixed bias property

Fuente: arXiv
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Main Authors: Rotnitzky, Andrea, Smucler, Ezequiel, Robins, James M.
Format: Preprint
Published: 2025
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author Rotnitzky, Andrea
Smucler, Ezequiel
Robins, James M.
author_facet Rotnitzky, Andrea
Smucler, Ezequiel
Robins, James M.
contents Bruns-Smith et al. (2025) established an algebraic identity between the one-step estimator and a specific outcome regression-type estimator for a class of parameters that forms a strict subset of the class introduced in Chernozhukov et al. (2022), assuming both nuisance functions are estimated as linear combinations of given features. They conjectured that this identity extends to the broader mixed bias class introduced in Rotnitzky et al. (2021). In this note, we prove their conjecture and further extend the result to allow one of the nuisance estimators to be non-linear. We also relate these findings to the work of Robins et al. (2007), who established other identities linking one-step estimators to outcome regression-type and IPW-type estimators.
format Preprint
id arxiv_https___arxiv_org_abs_2509_22452
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A note on the relation between one-step, outcome regression and IPW-type estimators of parameters with the mixed bias property
Rotnitzky, Andrea
Smucler, Ezequiel
Robins, James M.
Statistics Theory
Methodology
Bruns-Smith et al. (2025) established an algebraic identity between the one-step estimator and a specific outcome regression-type estimator for a class of parameters that forms a strict subset of the class introduced in Chernozhukov et al. (2022), assuming both nuisance functions are estimated as linear combinations of given features. They conjectured that this identity extends to the broader mixed bias class introduced in Rotnitzky et al. (2021). In this note, we prove their conjecture and further extend the result to allow one of the nuisance estimators to be non-linear. We also relate these findings to the work of Robins et al. (2007), who established other identities linking one-step estimators to outcome regression-type and IPW-type estimators.
title A note on the relation between one-step, outcome regression and IPW-type estimators of parameters with the mixed bias property
topic Statistics Theory
Methodology
url https://arxiv.org/abs/2509.22452