Resampled Regenerative Estimators

We discuss some estimators for simulations of processes having multiple regenerative sequences. The estimators are obtained by resampling trajectories without and with replacement, which correspond to a type of U-statistic and a type of V-statistic, respectively. The U-statistic estimator turns out to be equivalent to the permuted regenerative estimator, which we previously proposed, but the V-statistic estimator is new. We compare analytically some properties of these estimators and the semiregenerative estimator. We show that when estimating the second moment of a cycle reward, the semiregenerative estimator has positive bias, which is strictly larger than the (positive) bias of the V-statistic estimator. The permuted estimator is unbiased. All of the estimators have the same asymptotic central limit behavior, with reduced asymptotic variance compared to the standard regenerative estimator. Some numerical results are included.