New methods for multiple comparison procedures

点击翻译按钮获取中文摘要

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.