New methods for multiple comparison procedures

这个研究项目有三个方面。第一个领域将涉及大规模多重测试的错误发现率（FDR）控制相关问题，这是现代统计学中具有挑战性和核心的领域之一。第二个领域将涉及家庭误差率控制的复杂单调剂量反应研究。第三个领域将涉及在订单限制下有信心的统计分类。******在第一个领域，复杂和大规模的多重测试问题涉及各种结构。例如，单调剂量-反应微阵列实验需要检测由化合物剂量水平增加引起的基因表达趋势。比较两个独立实验的结果是许多研究人员的共同兴趣，每个实验都涉及数百或数千个假设检验。我将修改我的假覆盖率（FCR）的工作，它是单调剂量反应微阵列实验中非覆盖构建区间的预期比例，以考虑定向FDR控制。我将考虑剂量反应微阵列实验中FCR的控制，在治疗至少与控制一样好的先验知识下。这种类型的先验信息被称为简单树排序，可能来自过去的经验或主题知识。利用Sun等人（2006）的分层FDR思想，我将开发分层多重测试程序和异质多项分布的FCR控制。我将使用非参数经验贝叶斯框架来识别在两个独立实验中差异表达的基因。******最小有效剂量的确定，即作用超过零剂量的最低剂量水平，在药物开发中非常重要。在第二个领域，我将开发一种新的间隔程序，通过分区原则同时确定单调剂量反应研究中几组中每组的最小有效剂量。******订单限制信息的利用提高了统计推断的效率这一事实是有据可查的。该研究计划的第三个领域将是在订单限制下的统计分类。******开发的许多方法受到实际应用的启发，将适用于大规模统计问题和具有顺序限制的复杂剂量-反应研究。统计分类在医学、工程和社会科学等领域有着广泛的应用。该提案将开发新的分类规则，利用顺序限制推理的思想来利用平均值之间的潜在顺序。该研究项目将培养本科生和研究生，帮助他们有效地参与被大数据淹没的信息时代。

This research program has three areas. The first area will involve false discovery rate (FDR) control related problems for large-scale multiple testing, one of the challenging and central fields in modern statistics. The second area will involve complex monotone dose-response studies for familywise error rate control. The third area will involve statistical classification with confidence under order restriction.******In the first area, complex and large-scale multiple testing problems involve various structures. For example, monotone dose-response microarray experiments need to detect trends in gene expressions caused by increasing dose levels of a compound. It is of common interest for many researchers to compare the results of two independent experiments, where each experiment involves hundreds or thousands of hypothesis tests. I will modify my work of false coverage rate (FCR), which is the expected proportion of non-covering constructed intervals, for monotone dose-response microarray experiments to consider directional FDR control. I will consider the control of FCR in dose-response microarray experiments under the prior knowledge that treatments are at least as good as the control. This type of prior information, which is called simple tree ordering, may come from past experience or subject matter knowledge. Using Sun et al. (2006)'s stratified FDR idea I will develop stratified multiple testing procedures and FCR control with heterogeneous multinomial distributions. I will use a nonparametric empirical Bayes framework to identify genes that are differentially expressed in both of two independent experiments.******Identification of the minimum effective dose, which is the lowest dose level with an effect that exceeds that of the zero dose, is very important in drug development. In the second area, I will develop a new interval procedure to simultaneously identify the minimum effective dose in each of several groups under monotone dose-response studies through the partitioning principle.******The fact that the utilization of order restriction information increases the efficiency of statistical inference is well documented. The third area for this research program will be statistical classification with confidence under order restriction. ******Many of the methods developed are inspired by real applications and will be applicable to large-scale statistical problems and complex dose-response studies with order restrictions. Statistical classification has many applications in a wide range of fields including medicine, engineering, and social sciences. This proposal will develop new classification rules that exploit the underlying order among mean values by using ideas from order restricted inference. This research program will train both undergraduate and graduate students to help them participate effectively in an information era overwhelmed by big data.