Statistical Inference on Ordered Alternatives and Changepoint Hypotheses

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Testing the monotone alternative in the sequence of normal means has been extensively investigated by Barthoromew and others since 1960's. We combined the stream to that of the changepoint hypothesis and extended it to the ordered alternatives in the first and second order differences in normal means, which are called the convexity and the sigmoidicity hypotheses, respectively and essential in the nonparametric dose-response analysis. We developed those methods based on the cumulative efficient scores differently from the main stream of the maximum likelihood method, which are easier to be extended to more complicated cases including the two-way analysis of variance model and contingency tables. As such extensions we could especially develop a method of profile analysis of subjects based on 24 hours measurements of blood pressure and also an exact testing procedure for the association between the disease and alleles at highly polymorphic loci with particular interest in the haplotype analysis.We also developed an exact and efficient algorithm for calculating the level probabilities of the restricted likelihood ratio test and made it much easier to apply the method. Other interesting result obtained is to combine one- and two-sided simultaneous confidence intervals to a single procedure.