Methods of Overlapping Batch Variances for Simulation Output Analysis

• Main Authors: Chia-Shuen Yeh, 葉嘉舜
• Other Authors: Wei-Ning Yang
• Format: Others
• Language: en_US
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/24557865323971599032

碩士 === 中原大學 === 工業工程研究所 === 90 === ABSTRACT Methods of Overlapping Variances for Simulation Output Analysis Chia-Shuen Yeh We consider the case that the performance measure of interest is a population variance, which can be estimated by the sample variance (with denominator being the number of data) based on a set of identically distributed but correlated data. The research problem is to estimate the variance of the sample variance, for purposes such as constructing confidence intervals. The batching method for output analysis with correlated data is easy to implement and requires only a single long run in the simulation experiment. Intensive research has been devoted to the problem of estimating the variance of the sample mean, but little to the sample variance, for the case that the interested performance measure is a mean. The batching method estimates the variance of the sample variance by dividing the observations into several batches. Sample variances, called batch variances, of batched data are computed for each batch. The variance estimator for the sample variance is therefore a function of the batch variances. Depending on whether the batches overlap or not, the estimator is defined ferently as nonoverlapping batch variance (NBV) and overlapping batch variance (OBV) estimators, respectively. By viewing the sample variance as a sample mean of the quadratic terms, we show that the asymptotic results for the method of batch variances work in the same way as those for the method of batch means with the output data defined as the quadratic terms. The asymptotic results consist of three parts: convergence rate, constant multiplier, and data properties. We show that both methods have the same convergence rate and constant multiplier and that the data properties for the method of batch variances are the analogous properties for batch means whose data are quadratic terms. The proofs are provided for NBV estiamtors of linear processes. For OBV estimators, we assume that the asymptotic ratios between OBV and NBV are the same as those for batch means; hence, the OBV estimator has the proposed asymptotic results. The asymptotic bias for the first-order-moving-average process is computed as an evidence. In addition, we consider the method of dynamic NBVs (DNBVs) for the cases that the computer storage is small compared to the number of observations and that the number of observations is unknown in advance. We propose an approach of storing the batch variances dynamically and show that the asymptotic results for batch-mean estimators remain applicable to DNBV estimators. Keywords: Dynamic batch means; nonoverlapping batch means; optimal batch size; overlapping batch means; samplevariance; simulation output analysis