A Multivariate Goodness-of-Fit Test for Stochastically Ordered Distributions

摘要

There arc ;i [lumber of nonparnnielrie procedures known for testing goodness-of-fil in the imivariute wise. Similiir procedures can be derived for testing goodness-of-fit in the multivariate case through an application of the theory of statistically equivalent blocks (SHB). The SHI) transform:* the data into coverages which arc distributed as spneings from a uniform distribution on [0,1], under the null hypothesis. In this paper, we present a niullivariate nonparanielrie lest of goodness-of-fit based on the SKI) when the imillivarialc distributions under the null hypothesis and the alternative hypothesis are "weakly" ordered. Hmpirical results are given on the performance of the proposed test in an application to the problem of assessing the reliability of a p-component system.