Nearest neighbour imputation under single index models

ABSTRACT

A popular imputation method used to compensate for item nonresponse in sample surveys is the nearest neighbour imputation (NNI) method utilising a covariate to defined neighbours. When the covariate is multivariate, however, NNI suffers the well-known curse of dimensionality and gives unstable results. As a remedy, we propose a single-index NNI when the conditional mean of response given covariates follows a single index model. For estimating the population mean or quantiles, we establish the consistency and asymptotic normality of the single-index NNI estimators. Some limited simulation results are presented to examine the finite-sample performance of the proposed estimator of population mean.

KEYWORDS:

• Asymptotic normality
• curse of dimensionality
• imputation
• mean
• quantiles
• SAVE

Acknowledgements

We would like to thank two referees for their comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China grants 11831008 and 11871287, the U.S. National Science Foundation grants DMS-1612873 and DMS-1914411, the Natural Science Foundation of Tianjin (18JCYBJC41100) and the Fundamental Research Funds for the Central Universities.

Notes on contributors

Jun Shao

Dr Jun Shao holds a PhD in statistics from the University of Wisconsin-Madison. He is a professor of statistics at the University of Wisconsin-Madison and East China Normal University. His research interests include variable selection and inference with high dimensional data,sample surveys, and missing data problems.

Lei Wang

Dr Lei Wang holds a PhD in statistics from East China Normal University. He is an assistant professor of statistics at Nankai University. His research interests include empirical likelihood and missing data problems.