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Primary Submission Category: Propensity Scores

When is the estimated propensity score better? High-dimensional analysis and bias correction

Authors: Fangzhou Su, Peng Ding, Wenlong Mou, Martin Wainwright,

Presenting Author: Fangzhou Su*

Anecdotally, using an estimated propensity score is superior to the
true propensity score in estimating the average treatment effect
based on observational data. However, this claim comes with several
qualifications: it holds only if propensity score model is correctly
specified and the number of covariates $d$ is small relative to the
sample size $n$. We revisit this phenomenon by studying the inverse
propensity score weighting (IPW) estimator based on a logistic model
with a diverging number of covariates. We first show that the IPW
estimator based on the estimated propensity score is consistent and
asymptotically normal with smaller variance than the oracle IPW
estimator (using the true propensity score) emph{if and only if} $n
gtrsim d^2$. We then propose a debiased IPW estimator that
achieves the same guarantees in the regime $n gtrsim d^{3/2}$. Our
proofs rely on a novel non-asymptotic decomposition of the IPW error
along with careful control of the higher order terms.