Kernel machine in semiparametric regression with nonignorable missing responses

Missing data is prevalent in many fields. Among all missing mechanisms, nonignorable missing data is more challenging for model identification. In this paper, we propose a semiparametric regression model estimation method with nonignorable missing responses. To be specific, we first construct a parametric model for the propensity score and apply the generalized method of moments to obtain the estimated propensity score. For nonignorable missing responses, based on the inverse probability weighting approach, we propose the penalized garrotized kernel machine method to flexibly depict the complex nonlinear relationships between the response and the predictors, allow for interactions between the predictors, and eliminate the redundant variables automatically. The cyclical coordinate descent algorithm is provided to solve the corresponding optimization problems. Numerical results and real data analysis indicate that our proposed method achieves better prediction performance compared with the competing ones.