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Vietnam Journal of Mathematics 36:3(2008) 291-304  Nonparametric Statistical Inference for Umbrella Trend Alternative among Multinomial Populations Yanqin Feng Abstract.  Umbrella ordering is important in dose-response experiment. This paper treats the problem of comparing umbrella pattern treatment effects. Under an $m\times r$ table, for testing the equality against the umbrella ordering alternative, this article introduces a model-free test method by using likelihood ratio test statistic and gives the asymptotic distribution of this statistic, which is a chi-bar-squared distribution. A real example will be used to illustrate our theoretical result.   2000 Mathematics Subject Classification: 62J10. Keywords: Stochastic ordering, chi-bar-squared distribution, likelihood ratio test, umbrella ordering, asymptotic distribution.

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