Statistical validation of simulation models of observable systems
In this paper; for validating computer simulation models of real, observable systems, an uniformly most powerful invariant (UMPI) test is developed from the generalized maximum likelihood ratio (GMLR). This test can be considered as a result of a new approach to solving the Behrens-Fisher problem when covariance matrices of two multivariate normal populations (compared with respect to their means) are different and unknown. The test is based on invariant statistic whose distribution, under the null hypothesis, does not depend on the unknown (nuisance) parameters. The sample size and threshold of the UMPI test are determined from minimization of the weighted sum of the model builder's risk and the model user's risk. The proposed test could result in the saving of sample items, if the items of the sample are observed sequentially. In this paper, we present the exact form of the proposed curtailed procedure and examine the expected sample size savings under the null hypothesis. The sample size savings can be bounded by a constant, which is independent of the sample size. Tables are given for the expected sample size savings and maximum sample size saving under the null hypothesis for a range of significance levels (a), dimensions (p) and sample sizes (n). The curtailed test considered in this paper represents improvement over the noncurtailed or standard fixed sample tests.
simulation systems risk cybernetics