Jackknife variance estimation in the presence of imputed data

Abstract

Variance estimation in the presence of imputed data has been widely studied in the literature. It is well known that treating the imputed values as if they were observed could lead to serious underestimation of the variance of the imputed estimator. Several approaches/techniques have been developed in recent years. In particular, Rao and Shao (1992) have proposed an adjusted jackknife that works well when the sampling fraction is small. However, in many situations, this condition is not satisfied. As a result, the Rao-Shao adjusted jackknife may lead to invalid variance estimators. To overcome this problem, Lee, Rancourt and Särndal (1995) have proposed a simple correction to the Rao-Shao adjusted jackknife. In this presentation, we discuss the properties of the resulting variance estimator under stratified simple random sampling without replacement. Also, using the reverse approach developed by Shao and Steel (1999), we consider another variance estimator that works well when the sampling fractions are not negligible. The case of unequal probability sampling designs such as proportional-to-size-designs will be briefly discussed. With Frédéric Picard (Université de Montréal & Statistics Canada )