Journal
BIOMETRIKA
Volume 105, Issue 1, Pages 199-213Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asx069
Keywords
Average treatment effect; Eigenvalue optimization; Reproducing-kernel Hilbert space; Sobolev space
Funding
- U.S. National Science Foundation
- National Heart, Lung, and Blood Institute of the U.S. National Institutes of Health
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1806063] Funding Source: National Science Foundation
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Covariate balance is often advocated for objective causal inference since it mimics randomization in observational data. Unlike methods that balance specific moments of covariates, our proposal attains uniform approximate balance for covariate functions in a reproducing-kernel Hilbert space. The corresponding infinite-dimensional optimization problem is shown to have a finite-dimensional representation in terms of an eigenvalue optimization problem. Large-sample results are studied, and numerical examples show that the proposed method achieves better balance with smaller sampling variability than existing methods.
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