Deep Transformation Model

We consider a nonparametric transformation model with weak assumptions, which encompasses many popular models as special cases. A rank-based deep neural network (DNN) estimation approach is developed, with a loss function significantly different from the existing ones.

It can accommodate outliers in response, which is a robustness property not broadly shared. For computational feasibility, we propose a double rectified linear unit (DReLU)-based estimator. To accommodate a diverging number of input variables and/or noises, we propose variable selection based on group penalization.