Variance estimation after Kernel Ridge Regression Imputation

Hengfang Wang, Jae Kwang Kim

Keywords: Reproducing Kernel Hilbert Space, Missing data, Nonparametric function estimation, Uncertainty quantification

Abstract: Imputation is a popular technique for handling missing data. Variance estimation after imputation is an important practical problem in statistics. In this paper, we consider variance estimation of the imputed mean estimator under the kernel ridge regression imputation. We consider a linearization approach which employs the covariate balancing idea to estimate the inverse of propensity scores. The statistical guarantee of our proposed variance estimation is studied when a Sobolev space is utilized to do the imputation, where $\sqrt{n}$-consistency can be obtained. Synthetic data experiments are presented to confirm our theory.