Estimation Techniques for Nonlinear Functions of the Steady-State Mean in Computer Simulation

A simulation study consists of several steps such as data collection, codingand model verification, model validation, experimental design, output data analysis,and implementation. Our research concentrates on output data analysis. In this field,many researchers have studied how to construct confidence intervals for the mean uof a stationary stochastic process. However, the estimation of the value of a nonlinearfunction f(u) has not received a lot of attention in the simulation literature. Towardsthis goal, a batch-means-based methodology was proposed by Munoz and Glynn (1997).Their approach did not consider consistent estimators for the variance of the pointestimator for f(u). This thesis, however, will consider consistent variance estimationtechniques to construct confidence intervals for f(u). Specifically, we propose methodsbased on the combination of the delta method and nonoverlapping batch means(NBM), standardized time series (STS), or a combination of both. Our approachesare tested on moving average, autoregressive, and M/M/1 queueing processes. Theresults show that the resulting confidence intervals (CIs) perform often better thanthe CIs based on the method of Munoz and Glynn in terms of coverage, the mean oftheir CI half-width, and the variance of their CI half-width.