Deep Neural Networks Guided Ensemble Learning for Point Estimation

In modern statistics, interests shift from pursuing the uniformly minimum variance unbiased estimator to reducing mean squared error (MSE) or residual squared error. Shrinkage-based estimation and regression methods offer better prediction accuracy and improved interpretation. However, the characterization of such optimal statistics in terms of minimizing MSE remains open and challenging in many problems, for example, estimating the treatment effect in adaptive clinical trials with pre-planned modifications to design aspects based on accumulated data. From an alternative perspective, we propose a deep neural network based automatic method to construct an improved estimator from existing ones. Theoretical properties are studied to provide guidance on applicability of our estimator to seek potential improvement. Simulation studies demonstrate that the proposed method has considerable finite-sample efficiency gain compared to several common estimators. In the Adaptive COVID-19 Treatment Trial (ACTT) as a motivating example, our ensemble estimator essentially contributes to a more ethical and efficient adaptive clinical trial with fewer patients enrolled. The proposed framework can be generally applied to various statistical problems, and can serve as a reference measure to guide statistical research.