A Stochastic Minimum Distance Test for Multivariate Parametric Models
The Annals of Statistics · 1989 · Volume 17 · Issue 1
Abstract
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.
Keywords
62E20, 62H15, bootstrap, Goodness-of-fit test, minimum distance test, Stochastic procedure, stochastic search
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