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A stochastic minimum distance test for multivariate parametric models. (English) Zbl 0684.62041
Summary: Stochastic procedures are randomized statistical procedures which are functions of the observed sample and of one or more artificially constructed auxiliary samples. As the size of the auxiliary samples increases, a stochastic procedure becomes nearly nonrandomized.
The stochastic test of this paper arises as a numerically feasible approximation to a natural minimum distance goodness-of-fit test for multivariate parametric models. The distance being minimized here is the half-space metric for probabilities on a Euclidean space. It is shown that the various approximations used in constructing the stochastic test and its critical values do not detract from its first-order asymptotic performance.

MSC:
62H15 Hypothesis testing in multivariate analysis
62E20 Asymptotic distribution theory in statistics
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