On Developing Overlapping Batch Means Confidence Interval Procedures

Nonoverlapping batch means (NBM) is the most common basis for confidence-interval procedures (CIPs) for the mean of a steady-state time series. Meketon and Schmeiser (1985) introduce overlapping batch means (OBM) as an alternative to NBM for estimating the standard error of the sample mean. Despite OBM's inherent efficiency, because the OBM statistic does not approach normality via the chi-squared distribution, no OBM CIP was ever introduced until Yeh and Schmeiser (2014b).This proposal is essentially an extended and cumulative line of research from Yeh and Schmeiser (2014b). The difficulty arising from developing an OBM CIP for the mean of a steady-state time series is that the sampling distribution of the OBM variance estimate is unknown. Pretending that the sampling distribution of the OBM estimate is chi squared in Yeh and Schmeiser (2014b), they determine numerically the degree of freedom to be used in the OBM CIP by fitting the second moment of the OBM estimate with that of the chi-squared distributionInstead of using a crude approximation for the sampling distribution for the OBM estimate, we would like to determine the exact asymptotic sampling distribution of the OBM estimate in developing a good OBM CIP. As indicated in Yeh and Schmeiser (2014a), validity of a CIP which can be achieved by using the exact sampling distribution in CIPs is crucial in developing a good CIP.The ultimate goal of this proposed research is twofold: to develop a good OBM CIP, and to advocate the OBM CIP by establishing a solid theoretical background for it. We cordially believe that OBM is the most efficient method for estimating the standard error of the sample mean among cancelation methods. It deserves much more attention from academia and practiceas well.