Balanced repeated replication variance estimators for survey data under imputation.

Abstract

Imputation is commonly used for missing data in sample surveys. Usually the imputed values are treated as true values and variance estimates are computed using standard variance formulas. But this procedure can lead to serious underestimation of the true variance. Rao and Shao (1992) proposed a new consistent jackknife variance estimator based on adjusting the imputed values. This thesis applies their idea to construct two adjusted Balanced Repeated Replication (BRR) variance estimators for stratified multistage surveys. Under a uniform response mechanism, the adjusted BRR variance estimators are shown to be consistent for a particular simple hot deck imputation and ratio hot deck imputation. Also, the relationship between jackknife variance estimators and BRR variance estimators which was established by Rao and Wu (1985) for completed data set, is shown to be still held for data set with imputed values. The performances of these variance estimates are compared through some simulation studies.