RETURN-STATE INDEPENDENT QUANTITIES IN REGENERATIVE-SIMULATION

An important parameter of the regenerative method of simulation output analysis is the choice of return state used for blocking observations . Computational experience has shown that the statistical properties o f estimators based on different regeneration points can vary widely. I n this paper we study the limiting joint distribution of the normalize d regenerative point and standard-deviation estimators for general sta te-space Markov chains. The asymptotic covariance between the point an d standard-derivation estimators is shown to be the same for all retur n states, and the quantity is related to the normalized skewness of th e partial sums of the chain. Since the covariance is constant, it foll ows that the choice of return state that minimizes the asymptotic vari ance of the standard-deviation estimator will maximize the correlation between the point and standard-deviation estimator. Consideration of asymptotic variance and covariance alone suggests that confidence inte rvals have the best coverage probabilities if the asymptotic variance of the standard-deviation estimator is minimized (thereby maximizing t he correlation).