Oracle-efficient estimation for the mean function of missing covariate data based on noparametrically estimated selection probabilities

Abstract

A weighted local linear estimator for the mean function is constructed based on nonparametrically estimated selection probabilities when covariates are missing at random. The weighted estimator is shown to be oracle-efficient, meaning it is uniformly as efficient as the infeasible estimator that uses the true selection probabilities assumed to be known as a prior. By applying oracle efficiency and the extreme value distribution of the weighted local linear estimator, asymptotically accurate simultaneous confidence bands for the mean function are derived. This approach avoids the risk of model misspecification for the missingness mechanism. Simulation studies are conducted to examine the finite sample performance, which supports the asymptotic results. The proposed methods are illustrated through the analysis of two real data sets.

Keywords:

• Missing data
• oracle-efficient
• simultaneous confidence band
• weighted local linear regression

Acknowledgements

We thank the two reviewers for their helpful comments and suggestions that have significantly improved the original version of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported in part by Zhejiang Provincial Philosophy and Social Sciences Planning Project 24NDJC301YBMS, the National Statistical Science Research Key Program of China 2021LZ01, the Fundamental Research Funds for the Provincial Universities of Zhejiang XR202303, the Characteristic & Preponderant Discipline of Key Construction Universities in Zhejiang Province (Zhejiang Gongshang University–Statistics), and the Simons Foundation Mathematics and Physical Sciences Program Award 499650.