Shen Xiaoxi, Jiang Chang, Sakhanenko Lyudmila, Lu Qing
Department of Biostatistics, University of Florida, Gainesville, FL, USA.
Department of Statistics and Probability, Michigan State University, East Lansing, MI, USA.
Stat Probab Lett. 2021 Jul;174. doi: 10.1016/j.spl.2021.109100. Epub 2021 Mar 26.
Neural networks have become increasingly popular in the field of machine learning and have been successfully used in many applied fields (e.g., imaging recognition). With more and more research has been conducted on neural networks, we have a better understanding of the statistical proprieties of neural networks. While many studies focus on bounding the prediction error of neural network estimators, limited research has been done on the statistical inference of neural networks. From a statistical point of view, it is of great interest to investigate the statistical inference of neural networks as it could facilitate hypothesis testing in many fields (e.g., genetics, epidemiology, and medical science). In this paper, we propose a goodness-of-fit test statistic based on neural network sieve estimators. The test statistic follows an asymptotic distribution, which makes it easy to use in practice. We have also verified the theoretical asymptotic results via simulation studies and a real data application.
神经网络在机器学习领域越来越受欢迎，并已成功应用于许多应用领域（如成像识别）。随着对神经网络的研究越来越多，我们对神经网络的统计特性有了更好的理解。虽然许多研究专注于界定神经网络估计器的预测误差，但对神经网络的统计推断的研究却很有限。从统计学的角度来看，研究神经网络的统计推断非常有趣，因为它可以促进许多领域（如遗传学、流行病学和医学）的假设检验。在本文中，我们提出了一种基于神经网络筛估计器的拟合优度检验统计量。该检验统计量遵循渐近分布，这使得它在实际应用中易于使用。我们还通过模拟研究和实际数据应用验证了理论渐近结果。
