Experimental Evaluation of Integrated Path Estimators

Abstract

We describe the results of numerical experiments evaluating the efficiency of variance estimators based on integrated sample paths. The idea behind the estimators is to compute a vector of integrated paths and combine them to form an estimator of the time-average variance constant that is used, for example, in the construction of confidence intervals. When used in conjunction with batching, the approach generalizes the method of non-overlapping batch means. Compared with non-overlapping batch means, the estimators require longer to compute, have smaller variance and larger bias. We show that for long enough simulation run lengths, the efficiency (the reciprocal of running time multiplied by mean-squared error) of integrated path estimators can be much greater than that of non-overlapping batch means; the numerical experiments show an efficiency improvement by up to a factor of ten.