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- W4313447741 abstract "We consider the problem of constructing minimax rate-optimal estimators for a doubly robust nonparametric functional that has witnessed applications across the causal inference and conditional independence testing literature. Minimax rate-optimal estimators for such functionals are typically constructed through higher-order bias corrections of plug-in and one-step type estimators and, in turn, depend on estimators of nuisance functions. In this paper, we consider a parallel question of interest regarding the optimality and/or sub-optimality of plug-in and one-step bias-corrected estimators for the specific doubly robust functional of interest. Specifically, we verify that by using undersmoothing and sample splitting techniques when constructing nuisance function estimators, one can achieve minimax rates of convergence in all Holder smoothness classes of the nuisance functions (i.e. the propensity score and outcome regression) provided that the marginal density of the covariates is sufficiently regular. Additionally, by demonstrating suitable lower bounds on these classes of estimators, we demonstrate the necessity to undersmooth the nuisance function estimators to obtain minimax optimal rates of convergence." @default.
- W4313447741 created "2023-01-06" @default.
- W4313447741 creator A5013076039 @default.
- W4313447741 creator A5015580096 @default.
- W4313447741 date "2022-12-30" @default.
- W4313447741 modified "2023-10-18" @default.
- W4313447741 title "On Undersmoothing and Sample Splitting for Estimating a Doubly Robust Functional" @default.
- W4313447741 doi "https://doi.org/10.48550/arxiv.2212.14857" @default.
- W4313447741 hasPublicationYear "2022" @default.
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