Focused vector information criterion model selection and model averaging regression with missing response

In this paper, a focused vector information criterion for model selection and model averaging is considered for the linear model with missing response. Based on the focused information criterion of Hjort and Claeskens (J Am Stat Assoc 98:879–945, 2003) and imputation idea, a frequentist model averaging estimator for a focused vector of a linear model is proposed, and the estimator is shown to be root-n consistent and asymptotical normal. In addition, the proposed focused vector information criterion is designed for focused multidimensional parameter, which is a little different from conventional focused information criterion for one dimensional focused parameter. A model averaging based confidence interval estimation method and estimation of the mean of the response are also proposed. A simulation study is conducted to investigate the performance of the proposed estimator with finite sample sizes and a real data example is presented to illustrate its application in practice.