Bootstrap methods for imputed data from regression, ratio and hot‐deck imputation

Abstract

AbstractItem non‐response in sample surveys is usually addressed by imputation. A bootstrap method that treats the imputed values as if they were observed generally leads to variance estimates that are too small. Shao & Sitter (1996) introduced a bootstrap method in this context, which leads to consistent variance estimators when the sampling fraction is small. In the context of stratified simple random sampling, we introduce the independent bootstrap, which is valid even when the sampling fraction is large. It consists of modifying a bootstrap method for sample surveys, of independently generating the response status of each unit, and of imputing the non‐respondents in the bootstrap sample. We pay special attention to the bootstrap survey weights approach of Rao, Wu, & Yue (1992). The Canadian Journal of Statistics 42: 142–167; 2014 © 2014 Statistical Society of Canada