  Most existing studies on the double/debiased machine learning method
concentrate on the causal parameter estimation recovering from the first-order
orthogonal score function. In this paper, we will construct the
$k^{\mathrm{th}}$-order orthogonal score function for estimating the average
treatment effect (ATE) and present an algorithm that enables us to obtain the
debiased estimator recovered from the score function. Such a higher-order
orthogonal estimator is more robust to the misspecification of the propensity
score than the first-order one does. Besides, it has the merit of being
applicable with many machine learning methodologies such as Lasso, Random
Forests, Neural Nets, etc. We also undergo comprehensive experiments to test
the power of the estimator we construct from the score function using both the
simulated datasets and the real datasets.
