Topics in multiple comparison procedures and variable selection

这项研究计划有三个方面。第一个领域将涉及通过同时推断进行低剂量风险评估。第二个领域将涉及剂量-反应微阵列分析和样本大小确定，以控制错误发现率。第三个领域将涉及稳健的变量选择。 在定量风险分析中，一个众所周知的问题是，缺乏低剂量信息或对任何有限的低剂量数据应用不当可能导致不可靠的推断。我将使用三段置信带而不是目前使用的双曲线带来构建与非定量数据和定量数据的特定风险相关的基准剂量的更清晰的下置信限。剂量反应微阵列实验的一个目标是检测由增加化合物剂量水平引起的基因表达的趋势。我将把我早期关于传统单调剂量-反应研究的工作修改为剂量-反应微阵列实验。我将解决剂量响应微阵列实验中具有挑战性的多重性调节问题。我还将考虑在微阵列研究的对照分析中的处理中用于错误发现对照的样本量的确定。带有适当惩罚的惩罚最小二乘法被广泛地应用于回归中的同时变量选择和系数估计。然而，惩罚最小二乘法的效率受到异常观测和重尾分布的不利影响。在高维数据的统计文献中，我将通过惩罚和基于组合惩罚的稳健变量选择来考虑基于排名的非线性模型。 第一个领域提出的新方法将为环境风险评估提供更准确的结果。第二个领域的结果将对新药开发和微阵列实验设计非常有用。第三个方面的研究结果将丰富变量选择研究。这一研究方案强调开发和传播新的统计方法，并为培训高素质人才提供了许多机会。

This research program has three areas. The first area will involve low dose risk estimation via simultaneous inference. The second area will involve dose-response microarray analysis and sample size determination for false discovery rate control. The third area will involve robust variable selection. It is a well-known concern in quantitative risk analysis that lack of low dose information or poor application of any limited low dose data can lead to unreliable inferences. I will use the three-segment confidence bands instead of the currently used hyperbolic bands to construct sharper lower confidence bound on the benchmark dose associated with a particular risk for both nonquantal data and quantal data. One goal of dose-response microarray experiments is to detect trends in gene expressions caused by increasing dose levels of a compound. I will modify my earlier work on traditional monotone dose-response studies to dose-response microarray experiments. I will tackle the challenging multiplicity adjustment problem in dose-response microarray experiments. I will also consider sample size determination for false discovery control in treatments with a control analysis for microarray studies. The penalized least squares method with some appropriately defined penalty is widely used for simultaneous variable selection and coefficient estimation in regression. However, the efficiency of the penalized least squares method is adversely affected by outlying observations and heavy-tailed distributions. I will consider rank-based nonlinear model via penalization and robust variable selection based on the combined penalization in the statistical literature for high dimensional data. The new methods proposed in the first area will provide more accurate results in enviromental risk assessment. The results in the second area will be very useful for new drug development and microarray experiment design. The results in the third area will enrich variable selection research. This research program emphasizes the development and dissemination of new statistical methods and provides many opportunities to train highly qualified personnel.