Consistency of overlapping batch variances

When the simulation point estimator is the sample variance, its standard error can be estimated using batch variances, which are analogous to batch means for the standard error of the sample mean. We suggest a modification to the definition of OBV for analytical tractability and to improve its statistical properties. We discuss conjectures about when overlapping batch variances (OBV) is consistent. In particular, we argue that OBV seems likely to be consistent (almost) whenever overlapping batch means (OBM) is consistent. Both the definition modification and the consistency conjecture seem relevant to all overlapping batch statistics (OBS) estimators where the point estimator can be interpreted as the mean of a related stochastic process.