Batching on Biased Estimators

Existing batching methods are designed to cancel the variability parameter but not the bias of estimators, and thus are applied typically in the setting of unbiased estimation. We provide a batching scheme that cancel out the bias and variability parameters of estimators simultaneously, yielding asymptotically exact confidence intervals for biased estimation problems. We apply our batching method to finite difference estimators. We extend our method to the multivariate case in constructing confidence regions. We validate our theory and analyze the effect of the number of batches through numerical examples.