Optimal averaging estimator of heterogeneous treatment effects for single-index models
摘要
In the estimation of heterogeneous treatment effects, model uncertainty often exists for reasons such as doubt about which variable or model should be used. To handle the model uncertainty, we offer a model averaging method by assembling the estimators obtained from multiple single-index models. We use J-fold cross-validation to choose averaging weights and investigate the asymptotic properties of the proposed method under two settings: (1) all candidate models are misspecified; and (2) candidate models include correct models. In the first setting, we show that our method has asymptotic optimality in the sense of achieving the lowest possible squared loss, and the selected weights can converge to the optimal weights. In the second setting, our proposed weighting scheme asymptotically assigns all weights to the correct models, which leads to a consistency of model averaging estimator. Two simulation studies and an empirical application are used to illustrate the merits of our method.