Observations of a stationary stochastic process can be transformed into a standardized time series. This paper presents a lemma giving the asymptotic properties of this standardized series under quite general conditions. In particular, the conditions are satisfied by stationary discrete-event simulations. Confidence intervals can be constructed using this lemma. For illustration, we develop two easily computed interval estimators for the process mean. When independent replications of the series are available, such as in computer simulation experiments, these interval estimators may be combined with the classical confidence interval estimator. These interval estimators also tend to compensate for simulation initialization bias if the sign of the bias is known. In an empirical study using three elementary simulated processes, the interval estimators presented here compare favorably with the classical interval estimator. In a recent paper, Goldsman and Schruben (Goldsman, D., L. Schruben. 1982. Asymptotic properties of some confidence interval estimators. Tech. Rep. 544, School of O.R.I.E., Cornell University, Ithaca, NY.) show that the asymptotic properties of the confidence intervals presented in this paper strictly dominate those of classical confidence intervals.

Statistical Computing fU)bert Sargent

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A general approach to testing for initialization bias in the mean of a simulation output series is presented. The output is transformed into a standardized test sequence that can be contrasted with a known limiting stochastic process. This transformation requires very little computation and the asymptotic theory is applicable to a wide variety of simulations. An initialization bias test is developed and several examples of its application are presented.

A procedure is proposed to promote the acceptance of a simulation model. The procedure actively involves potential users of the simulation. Several alterna tive approaches for the statistical analysis of the experimental results are suggested. Two contrasting experiences in applying the procedure to actual simulation projects are discussed.

We present a family of tests for detecting initialization bias in the mean of a simulation output series using a hypothesis testing framework. The null hypothesis is that the output mean does not change throughout the simulation run. The alternative hypothesis specifies a general transient mean function. The tests are asymptotically optimal based on cumulative sums of deviations about the sample mean. A particular test in this family is applied to a variety of simulation models. The test requires very modest computation and appears to be both robust and powerful.

We wish to estimate the variance of the sample mean from a continuous-time stationary stochastic process. This article expands on the results of a technical note (Goldsman and Schruben 1990) by using the theory of standardized time series to investigate weighted generalizations of Schruben's area variance estimator. We find a simple expression for the bias of the weighted area variance estimator, and we give weights which yield variance estimators with lower asymptotic bias than certain other popular estimators. We use the weighted area variance estimators to derive asymptotically valid confidence interval estimators (CIEs) for the mean of a stationary stochastic process. Although the weighted area CIEs have the same asymptotic expected value and variance of the length as Schruben's area CIE, we show that the new CIEs sometimes yield coverages which are closer to the nominal value.simulation output analysis, confidence intervals, standardized time series

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