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Activity Number:
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558
- Semi- or Nonparametric Modeling for Data with Complex Structure
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Type:
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Contributed
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Date/Time:
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Thursday, August 11, 2022 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #323089
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Title:
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Undersmoothing and Sample Splitting for Estimating Nonparametric Functionals
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Author(s):
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Sean McGrath* and Rajarshi Mukherjee
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Companies:
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Harvard University and Harvard T.H. Chan School of Public Health
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Keywords:
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Undersmoothing;
Sample splitting;
Functional estimation;
Bias correction;
Causal inference
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Abstract:
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We consider the problem of constructing simple rate-optimal estimators for nonparametric functionals such as causal effects and those arising from missing data problems. Minimax rate-optimal estimators in such settings are typically constructed through higher-order bias correction of plug-in and one-step type estimators. However such estimators are often complicated and depend on expressing higher-order semiparametric tangent spaces and influence functions. In this paper, we explore the necessity of such complicated constructions by considering a doubly robust functional that has gained popularity in causal studies. In particular, we show that systematic undersmoothing (for estimating nuisance functions such as outcome regression and propensity score for causal inference) and sample splitting (i.e., using separate subsamples to estimate different nuisance functions) can be used to construct minimax rate-optimal estimators. Specifically, we show that a simple plug-in estimator can be rate-optimal when using undersmoothing and sample splitting. We also illustrate that such sample splitting and undersmoothing can be suboptimal when using the popular doubly robust estimator.
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Authors who are presenting talks have a * after their name.
