Statistical Inference after Kernel Ridge Regression Imputation under item nonresponse
This work addresses statistical inference challenges in missing data analysis for researchers and practitioners, though it appears incremental as it builds on existing kernel ridge regression imputation methods.
The paper tackles variance estimation for kernel ridge regression imputation under item nonresponse, proposing a consistent estimator based on linearization and entropy methods, with root-n consistency established in Sobolev spaces and validated through synthetic experiments.
Imputation is a popular technique for handling missing data. We consider a nonparametric approach to imputation using the kernel ridge regression technique and propose consistent variance estimation. The proposed variance estimator is based on a linearization approach which employs the entropy method to estimate the density ratio. The root-n consistency of the imputation estimator is established when a Sobolev space is utilized in the kernel ridge regression imputation, which enables us to develop the proposed variance estimator. Synthetic data experiments are presented to confirm our theory.