Jackknife bias‐corrected variance estimation for the generalized regression estimator

Commonly used variance estimators for the generalized regression estimator (GREG) are based on Taylor linearization and jackknife. Traditionally, a jackknife GREG variance estimator is obtained by jackknifing GREG, which consists of computing GREG from each of several subsamples of the parent sample, and estimating the variance of the parent sample from the variability between the subsample GREG estimates. The jackknife technique can also be used for bias correction, which means that the jackknifing of GREG can be used to reduce the bias of GREG. Instead of jackknifing GREG, we propose to jackknife a variance estimator of GREG to obtain a bias‐corrected GREG variance estimator. We show that jackknifing a variance estimator can be performed as usual by viewing the variance estimator as the mean over a sample selected in a synthetic finite population with a sampling design having first‐order inclusion probabilities equal to the second‐order inclusion probabilities of the initial sampling design.