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In modern statistics, interests shift from pursuing the uniformly minimumvariance unbiased estimator to reducing mean squared error (MSE) or residualsquared error. Shrinkage based estimation and regression methods offer betterprediction accuracy and improved interpretation. However, the characterizationof such optimal statistics in terms of minimizing MSE remains open andchallenging in many problems, for example estimating treatment effect inadaptive clinical trials with pre-planned modifications to design aspects basedon accumulated data. From an alternative perspective, we propose a deep neuralnetwork based automatic method to construct an improved estimator from existingones. Theoretical properties are studied to provide guidance on applicabilityof our estimator to seek potential improvement. Simulation studies demonstratethat the proposed method has considerable finite-sample efficiency gain ascompared with several common estimators. In the Adaptive COVID-19 TreatmentTrial (ACTT) as an important application, our ensemble estimator essentiallycontributes to a more ethical and efficient adaptive clinical trial with fewerpatients enrolled. The proposed framework can be generally applied to variousstatistical problems, and can be served as a reference measure to guidestatistical research.

Deep Neural Networks Guided Ensemble Learning for Point Estimation