A Bootstrap Method for a Multiple-Imputation Variance Estimator in Survey Sampling

Lili Yu () and Yichuan Zhao
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Lili Yu: Department of Biostatistics, Epidemiology and Environmental Health Sciences, JPH College of Public Health, Georgia Southern University, Statesboro, GA 30460, USA
Yichuan Zhao: Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA

Stats, 2022, vol. 5, issue 4, 1-11

Abstract: Rubin’s variance estimator of the multiple imputation estimator for a domain mean is not asymptotically unbiased. Kim et al. derived the closed-form bias for Rubin’s variance estimator. In addition, they proposed an asymptotically unbiased variance estimator for the multiple imputation estimator when the imputed values can be written as a linear function of the observed values. However, this needs the assumption that the covariance of the imputed values in the same imputed dataset is twice that in the different imputed datasets. In this study, we proposed a bootstrap variance estimator that does not need this assumption. Both theoretical argument and simulation studies show that it was unbiased and asymptotically valid. The new method was applied to the Hox pupil popularity data for illustration.

Keywords: bootstrap; congeniality; domain mean; Rubin’s variance estimator; survey sampling (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2022
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