| Summary: | A simulation study consists of several steps such as data collection, coding
and 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 u
of a stationary stochastic process. However, the estimation of the value of a nonlinear
function f(u) has not received a lot of attention in the simulation literature. Towards
this 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 point
estimator for f(u). This thesis, however, will consider consistent variance estimation
techniques to construct confidence intervals for f(u). Specifically, we propose methods
based on the combination of the delta method and nonoverlapping batch means
(NBM), standardized time series (STS), or a combination of both. Our approaches
are tested on moving average, autoregressive, and M/M/1 queueing processes. The
results show that the resulting confidence intervals (CIs) perform often better than
the CIs based on the method of Munoz and Glynn in terms of coverage, the mean of
their CI half-width, and the variance of their CI half-width.
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