Localized Debiased Machine Learning: Efficient Inference on Quantile
Treatment Effects and Beyond
- URL: http://arxiv.org/abs/1912.12945v5
- Date: Wed, 17 Aug 2022 14:03:15 GMT
- Title: Localized Debiased Machine Learning: Efficient Inference on Quantile
Treatment Effects and Beyond
- Authors: Nathan Kallus, Xiaojie Mao, Masatoshi Uehara
- Abstract summary: We consider an efficient estimating equation for the (local) quantile treatment effect ((L)QTE) in causal inference.
Debiased machine learning (DML) is a data-splitting approach to estimating high-dimensional nuisances.
We propose localized debiased machine learning (LDML), which avoids this burdensome step.
- Score: 69.83813153444115
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We consider estimating a low-dimensional parameter in an estimating equation
involving high-dimensional nuisances that depend on the parameter. A central
example is the efficient estimating equation for the (local) quantile treatment
effect ((L)QTE) in causal inference, which involves as a nuisance the
covariate-conditional cumulative distribution function evaluated at the
quantile to be estimated. Debiased machine learning (DML) is a data-splitting
approach to estimating high-dimensional nuisances using flexible machine
learning methods, but applying it to problems with parameter-dependent
nuisances is impractical. For (L)QTE, DML requires we learn the whole
covariate-conditional cumulative distribution function. We instead propose
localized debiased machine learning (LDML), which avoids this burdensome step
and needs only estimate nuisances at a single initial rough guess for the
parameter. For (L)QTE, LDML involves learning just two regression functions, a
standard task for machine learning methods. We prove that under lax rate
conditions our estimator has the same favorable asymptotic behavior as the
infeasible estimator that uses the unknown true nuisances. Thus, LDML notably
enables practically-feasible and theoretically-grounded efficient estimation of
important quantities in causal inference such as (L)QTEs when we must control
for many covariates and/or flexible relationships, as we demonstrate in
empirical studies.
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