Deep Neural Networks Guided Ensemble Learning for Point Estimation

TL;DR

This paper introduces a deep neural network guided ensemble learning approach to improve point estimation by reducing mean squared error, demonstrating significant efficiency gains in simulations and adaptive clinical trials.

Contribution

It proposes a novel neural network based ensemble method for point estimation that enhances accuracy over traditional estimators, with theoretical analysis and practical applications.

Findings

Significant finite-sample efficiency improvements in simulations

Enhanced estimation accuracy in adaptive clinical trials

The framework is broadly applicable to various statistical problems

Abstract

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.