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In this paper, for identifying an observable process with one of several simulation models, a 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 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.

IDENTIFYING AN OBSERVABLE PROCESS WITH ONE OF SEVERAL SIMULATION MODELS VIA UMPI TEST