on strong consistency of the variance estimator
One way to construct a confidence interval for the mean constant of a stochastic process, is via consistent estimation of another parameter of the process, namely, the time-average variance constant. In this paper, we discuss strong consistency of the variance estimator for several methods of steady-state output analysis. These are; Batch Means (BM), Overlapping Batch Means (OBM), Spectral methods, and finally, Standardized Time Series (the area estimator of STS). A characterization of the spectral variance estimator is also presented; it is a generalization of OBM. Another estimator, which might be called Overlapping Area estimator, connects the area estimator with spectral methods.
consistency estimates interval mean stochastic process process timing paper method analysis standardization time series characterization general