Prediction using many samples with models possibly containing partially shared parameters

We consider prediction based on a main model. When the main model shares partial parameters with several other helper models, we make use of the additional information. Specifically, we propose a model averaging prediction (MAP) procedure that takes into account data related to the main model as well as data related to the helper models. We allow the data related to different models to follow different structures, as long as they share some common covariate effect. We show that when the main model is mis-specified, MAP yields the optimal weights in terms of prediction. Further, if the main model is correctly specified, then MAP will automatically exclude all incorrect helper models asymptotically. Simulation studies are conducted to demonstrate the superior performance of MAP. We further implement MAP to analyze a data set related to the probability of credit card default.