Published 30 October 2025

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Randomized experiments have been widely applied in empirical research. In modern applications, researchers often have access to a large number of covariates, and the methods of covariate adjustment are commonly employed. Although the theory of point estimation for causal effects with many covariates has been well-studied in recent literature, theoretical analyses on covariate selection and uncertainty quantification are still under-developed. In this paper, we propose a Mallows type optimal covariate selection criterion to minimize the approximate mean squared error of a cross-fitted point estimator for the average treatment effect, and develop a higher-order accurate standard error under moderately large number of covariates. Numerical studies based on Monte Carlo simulation and a real data example illustrate excellent finite sample performances of the proposed methods.