Model Averaging for Nonlinear Regression Models
针对参数和变量可能非线性的回归模型，提出非线性模型平均框架和权重选择准则NIC，证明其渐近无偏性和最优性，蒙特卡洛实验和工资预测案例显示该方法通常比传统方法预测误差更低。
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.