Statistical Inference on Ordered Alternatives and Changepoint Hypotheses

自20世纪60年代以来，Barthoromew等人对正态均值序列的单调替代检验进行了广泛的研究。我们将该流与变点假设流结合起来，并将其扩展到正态均值一阶和二阶差的有序选择，分别称为凸性和s型假设，它们在非参数剂量-反应分析中是必不可少的。与主流的最大似然方法不同，我们开发了基于累积有效分数的方法，这些方法更容易扩展到更复杂的情况，包括方差模型的双向分析和列联表。作为这样的扩展，我们可以特别开发一种基于24小时血压测量的受试者特征分析方法，以及一种精确的测试程序，用于疾病与高度多态性位点的等位基因之间的关联，特别是对单倍型分析感兴趣。我们还开发了一种精确而有效的算法来计算限制似然比检验的水平概率，使该方法的应用变得更加容易。另一个有趣的结果是将单侧和双侧同时置信区间结合到一个单一的过程中。

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.