STRONG CONSISTENCY OF THE VARIANCE ESTIMATOR IN STEADY-STATE SIMULATION OUTPUT ANALYSIS

In this paper, we study the problem of variance estimation in steady-s tate simulation output analysis. A confidence interval for the mean of an output sequence may be constructed using a (weakly) consistent est imator of the time-average variance constant of the process. Moreover, a strongly consistent estimator of the variance constant is required for fixed-width confidence-interval estimation procedures to be asympt otically valid. Here, we establish sufficient conditions to ensure str ong consistency of the estimator of the variance constant obtained by several widely used methods of steady-state simulation output analysis , namely, batch means, overlapping batch means, spaced batch means, an d standardized time series (area estimator). We also introduce the ove rlapping area estimator of the variance constant. The established suff icient conditions provide qualitative insight into the relation betwee n the correlation of the process and certain parameters (e.g., batch s ize) of the output method used.