Ridge Regression Model Averaging Based on Rp Criterion

Model selection is an important tool in statistical inference. However, it is useless with regard to the uncertainty inherent in the inference process. Multicollinearity is a common phenomenon in regression analysis, which can affect the prediction accuracy vastly. This paper introduces a model averaging method called Rp Model Averaging (RMA) to address these two problems simultaneously. Specifically, we use model averaging to deal with uncertainty and ridge estimator to deal with the multicollinearity. Asymptotic optimality of the proposed RMA estimator is derived under some regular conditions. The estimation procedure can be divided into a series of quadratic programming problems and hence easily implemented by existing softwares. Extensive simulation studies show that our proposed method has much better numerical performances in various scenarios. Our method is also employed to a real dataset to illustrate its validity.