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.

翻译：在本文中,我们建议从多维功能数据中为定位功能提供一个强有力的估计值。 拟议的估计值基于带有RELU激活功能的深神经网络; 同时, 估计值不那么容易受到外围观测和模型误差的影响。 对于任何多维功能数据, 我们为拟议的强健的深神经网络估计器提供统一的趋同率。 模拟研究显示了强健的深神经网络估计器在常规数据上的竞争性性能及其在含有异常数据的数据上的优异性。 拟议的方法还用于分析从阿尔茨海默氏病神经造影倡议数据库获取的阿尔茨海默氏病患者的2D和3D图像。