Sequential, nonsequential, and shrinkage inference techniques and applications

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This research proposes several improved methologies to deal with various statistical analysis problems of relevance in areas such as clinical trials, count data arising in toxicology, genetic linkage analysis of complex diseases, industrial quality control, and microarray data analysis.Specifically, I am proposing sequential methods for testing statistical hypotheses when the parameter space of interest is constrained. In general, if we know that parameters are restricted by some constraints then it is reasonable to expect that testing procedures incorporating the restrictions should be more powerful than those ignoring them.  An example of a model in which this happens is the one arising when testing whether or not a given gene is responsible for certain disease in the presence of other genes at different loci that may also be responsible for the disease. In such cases, the number of recombinants (a measure of the degree of linkage)   has a binomial mixture. Collecting data for such genetic studies requires many years and large financial support. The methods I am proposing will include hypotheses testing of this type and are expected to reduce the total sample needed for making decision. Moreover, the shrinkage sequential estimation methods proposed in this project are expected to reduce the sample size needed in DNA microarray data analysis while borrowing information across the genes. This is important, as the cost of a  microarray is quite high.Other methods in my proposal are empirical Bayes methods for the analysis of count data. These methods are also expected to be more efficient in estimating the average count and at the same time incorporating prior knowledge that is available in the form of auxiliary information (covariates or prognostic factors).