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 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 as compared with several common estimators. In the Adaptive COVID-19 Treatment Trial (ACTT) as an important application, 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 be served as a reference measure to guide statistical research.

翻译：在现代统计中,利益从追求统一的最低差异、无偏差估计值转向减少平均平差误差或残余平差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差