  We propose a semiparametric method to estimate the average treatment effect
under the assumption of unconfoundedness given observational data. Our
estimation method alleviates misspecification issues of the propensity score
function by estimating the single-index link function involved through Hermite
polynomials. Our approach is computationally tractable and allows for
moderately large dimension covariates. We provide the large sample properties
of the estimator and show its validity. Also, the average treatment effect
estimator achieves the parametric rate and asymptotic normality. Our extensive
Monte Carlo study shows that the proposed estimator is valid in finite samples.
We also provide an empirical analysis on the effect of maternal smoking on
babies' birth weight and the effect of job training program on future earnings.
