Jackknife Variance Estimation

There are two basic approaches to estimation of the variance for survey data: the Taylor linearization method and the resampling method. The resampling method includes the jackknife, balanced repeated replication (Fay's method as a variant), and bootstrap methods. The resampling method calls for creation of many replicate samples ("replicates" in short) taken from the original sample (called also the full or parent sample). Each resampling method uses a unique way of creating the replicates. Each replicate provides a point estimate of the population parameter of interest and the variability among the replicate estimates forms the basis of estimating the variance of the point estimate.

Let θ be the population parameter to be estimated from the sample and let R replicates be created, from which R replicate ...