Bootstrap inference for weighted nearest neighbors imputation

Abstract

An attractive approach to fill in substitute values for missing data is imputation. A number of methods are available in literature that can be used for the imputation of the missing data. However, it is not advisable to treat the imputed data just as the complete data. To apply the existing methods for analyzing the data, for example, to estimate the variance and/or statistical inference will probably produce invalid results because these methods do not account for the uncertainty of imputations. In this article, we present analytic techniques for inference from a dataset in which missing values have been replaced by the nearest neighbors imputation method. A simple and easy to use bootstrap algorithm that combines the nearest neighbors imputation with bootstrap resampling estimation, to obtain valid bootstrap inferences in a linear regression model is suggested. More specifically, imputing bootstrap samples in the exact same way as original data was imputed produces correct bootstrap estimates. Simulation results show the performance of our approach in different data structures.

Keywords:

• Bootstrapping
• Linear regression model
• Missing values
• Nearest neighbors imputation
• Single imputation

Acknowledgments

The authors are greatly thankful to Gerhard Tutz for his support. The initial results given in this paper were originally presented in the 22nd International Conference on Computational Statistics (COPMSTAT), Oviedo, Spain Ramzan et al (2016).