Inference for additive model at response random missing based on principal component imputation

Abstract

Abstract In this paper, we consider statistical inference for the additive model when the response is missing at random. The paper proposes a framework for statistical inference under missing data, which integrates basis function approximation and principal component imputed estimation equation (PCIEE). Inverse probability weighting is used to construct robust estimator. Under mild assumptions, the convergence rate of component function estimator is proved. In addition, when the sample size n tends to infinity, the PCIEE-based variable selection can select the real predictor. We also demonstrated the performance of PCIEE through numerical experiments.