Asymptotic Sampling Distributions of Overlapping Standardized Time Series Estimators

Batching is a classic approach for constructing confidence intervals of the sample meanobtained from a stationary data process. Typical batching estimators estimating the asymptoticvariance constant explicitly, whereas standardized time series (STS) estimates proposed bySchruben (1983) cancel out the asymptotic variance constant to construct confidence intervals.Nonoverlapping batch means (NBM) has long been the most-common used foundation for suchconfidence intervals. Meketon and Schmeiser (1985) introduce overlapping batch means (OBM)as a statistical efficient alternative to NBM for estimating the variance of the sample mean.Analogy to OBM estimators, Alexopoulos et al. (2007a) develop overlapping standardized timeseries (OSTS) estimates by applying the overlapping concept to the STS estimate. Because ofthe complexity of the sampling distribution of the OSTS estimate, the only OSTS basedconfidence interval procedure (CIP) is developed by Alexopoulos et al. (2007b).The original development of an OSTS CIP is based on the idea of approximating the samplingdistribution of an OSTS variance estimate by a sum of independent scaled chi squareddistributions and applying Satterthwaite’s method to obtain appropriate degree of freedom toapproximate the sampling distribution of an OSTS variance estimate.Our proposed research is a direct extension from Yeh and Schmeiser (2016). Different frommoment matching to approximate the sampling distribution of an OSTS estimate, we plan todetermine the exact asymptotic sampling distribution of OSTS estimates in developing goodOSTS CIPs. We adopt similar approach proposed by Yeh and Schmeiser (2016), which isapplied originally on the OBM estimate, to numerically determine the asymptotic samplingdistribution of an OSTS estimate. Our goal is to tabulate the distribution of each type of OSTSestimates, similarly to what is done for Student t distribution, for simulation practitioners to usein constructing OSTS confidence intervals.