Statistical inference of heterogeneous treatment effect based on single-index model

Abstract

The heterogeneous treatment effect (HTE) is estimated by using the semiparametric regression method. Firstly, a flexible semiparametric single-index model is considered by assuming the nonparametric link function and the interaction between treatment and covariates, and the index parameter vector and the unknown link function are estimated by using the rMAVE method. Then a HTE estimator can be obtained based on the estimators of index parameter vector and the link function. The consistency and asymptotic normality of the HTE estimator are established under some regularity conditions. Secondly, a hypothesis test is developed for the existence of HTE, and the bootstrap procedure is utilized to evaluate the null distribution of test statistic. Finally, simulation studies and a real data analysis are conducted to assess the performance of our proposed method.