Statistical Inference on Ordered Alternatives and Changepoint Hypotheses

有序替代方案和变点假设的统计推断

• 批准号: 11680321
• 负责人: HIROTSU Chihiro
• 金额: $ 2.37万
• 依托单位: Meisei University (2000-2001)The University of Tokyo (1999)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11680321/
• 关键词: Sigmoidicity; Optimal design of experiments; Restricted least squares method; Monotone hypothesis; Simultaneous Confidence intervals; Convexity; Changepoint hypothesis; Dose-response analysis; 傾向性仮説; 単調性; 凸性; S字性; 変化点モデル; 勾配変化モデル; 変曲点モデル; 凸

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.

Barthoromew 和其他人自 1960 年代以来就对正态均值序列中的单调替代进行了广泛的研究。我们将该流与变点假设相结合，并将其扩展到正常均值的一阶和二阶差值中的有序替代方案，这分别称为凸性假设和 sigmoidicity 假设，这在非参数剂量反应分析中是必不可少的。我们开发的这些方法基于累积有效分数，与主流的最大似然法不同，它们更容易扩展到更复杂的情况，包括方差模型和列联表的双向分析。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概况分析方法，以及一种针对高度多态性位点的疾病与等位基因之间关联的精确测试程序，尤其对单倍型分析感兴趣。我们还开发了一种精确有效的算法来计算限制似然比测试的水平概率，并使该方法的应用变得更加容易。获得的其他有趣结果是将一侧和两侧同时置信区间结合到单个过程中。

项目成果

Chihiro Hirotsu: "Simultaneous confidence intervals based on one-sided max t test"Statistics and Probability Letters. 49. 25-37 (2000)

Chihiro Hirotsu：“基于单侧最大 t 检验的同时置信区间”统计和概率信件。

Hirotsu,C.and Srivastava,M-S.: "Simultaneous confidence intervals base on one-sided max test"To appear in statistics and Probability Letters. (2000)

Hirotsu,C. 和 Srivastava,M-S.：“基于单侧最大检验的同时置信区间”出现在统计和概率快报中。

Hayter,A.J.,Miwa,T.and Liu,W.: "Combining the advantages of one-sided and two-sided procedures for comparing several treatments with a control"To appear in Journal of Statistical Plannning and Inference. (2000)

Hayter, A.J.、Miwa, T. 和 Liu, W.：“结合单侧和两侧程序的优点，将几种治疗方法与对照进行比较”发表在《统计规划与推断杂志》上。

Paul Somerville, Tetsuhisa Miwa, Wei Liu, A.J.Hayter: "Combining one-sided and two-sided confidence interval procedures for successive comparisons of ordered treatment effects"Biometrical Journal. 43. 533-542 (2001)

Paul Somerville、Tetsuhisa Miwa、Wei Liu、A.J.Hayter：“结合单侧和两侧置信区间程序来连续比较有序治疗效果”生物统计杂志。

Hirotsu,C.: "On an optimal design for an isotonic inference"To appear in J.statistical Planning and Inference. (2000)

Hirotsu,C.：“关于等渗推理的优化设计”出现在《统计规划与推理》杂志上。