Semiparametric ANCOVA using shape restrictions
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For the semiparametric ANCOVA model, shape restrictions are applied when there is only qualitative information about the relationship between response variable and the covariate. We obtain the least-squares fits of the shape-restricted ANCOVA model and conduct a beta test statistic for the balanced shape-restricted ANCOVA model, from which the hypotheses tests about the categorical variable I are performed. For the unbalanced shape- restricted ANCOVA, the hypotheses tests are p4rformed by two Bayesian analysis methods, I the Bayes credible interval method and Bayes factor. Both methods give reasonable test size and power, comparing with those of the related tests. The Bayes credible interval method is applied for simple hypotheses, and Bayes factor is a general method that can deal with any kind of hypotheses. Three real world examples represented, both the least-square shape-restricted fit and Bayes shape-restricted fit are obtained, and the hypotheses tests about the shape-restricted ANCOVA models are performed.