论文标题
多维功能数据的强大深度神经网络估计
Robust Deep Neural Network Estimation for Multi-dimensional Functional Data
论文作者
论文摘要
在本文中，我们从多维功能数据提出了一个可靠的位置函数估计器。所提出的估计器基于具有Relu激活函数的深神经网络。同时，估计器不太容易受到外围观察和模型 - 统计的影响。对于任何多维功能数据，我们为所提出的强大的深神经网络估计器提供均匀的收敛速率。仿真研究说明了强大的深神经网络估计器对常规数据的竞争性能及其在包含异常的数据上的出色性能。所提出的方法还用于分析从阿尔茨海默氏病神经成像倡议数据库中获得的阿尔茨海默氏病患者的2D和3D图像。
In this paper, we propose a robust estimator for the location function from multi-dimensional functional data. The proposed estimators are based on the deep neural networks with ReLU activation function. At the meanwhile, the estimators are less susceptible to outlying observations and model-misspecification. For any multi-dimensional functional data, we provide the uniform convergence rates for the proposed robust deep neural networks estimators. Simulation studies illustrate the competitive performance of the robust deep neural network estimators on regular data and their superior performance on data that contain anomalies. The proposed method is also applied to analyze 2D and 3D images of patients with Alzheimer's disease obtained from the Alzheimer Disease Neuroimaging Initiative database.
