Model Averaging for Nonlinear Regression Models
Yang Feng, Qingfeng Liu, Qingsong Yao, G. Q. Zhao
Abstract
This article considers the problem of model averaging for regression models that can be nonlinear in their parameters and variables. We consider a nonlinear model averaging (NMA) framework and propose a weight-choosing criterion, the nonlinear information criterion (NIC). We show that up to a constant, NIC is an asymptotically unbiased estimator of the risk function under nonlinear settings with some mild assumptions. We also prove the optimality of NIC and show the convergence of the model averaging weights. Monte Carlo experiments reveal that NMA leads to relatively lower risks compared with alternative model selection and model averaging methods in most situations. Finally, we apply the NMA method to predicting the individual wage, where our approach leads to the lowest prediction errors in most cases.