A weighted Jackknife method for clustered data

We propose a weighted delete-one-cluster Jackknife based framework for few clusters with severe cluster-level heterogeneity. The proposed method estimates the mean for a condition by a weighted sum of estimates from each of the Jackknife procedures. Influence from a heterogeneous cluster can be weighted appropriately, and the conditional mean can be estimated with higher precision. An algorithm for estimating the variance of the proposed estimator is also provided, followed by the cluster permutation test for the condition effect assessment. Our simulation studies demonstrate that the proposed framework has good operating characteristics.