Topics in multiple comparison procedures and variable selection

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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.