Inference strategies with applications and boostrapping

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This research is primarily concerned with the development of optimal tools to help in the analysis of complex data.  For example, how can DNA microarray data from various sources be combined, showing the promise of immense possible gains in statistical inferential accuracy?  How can uncertain prior information be incorporated into the current estimation process?  How can uncertainty concerning the appropriate statistical model-estimator to use in representing the data sampling process be dealt with?    These questions, and many more, can be better understood through appropriate statistical inferential tools.   The proposed research  demonstrates well-defined data-basesd estimation techniques. The focus of this research program is on the development and application of statistical inference methodologies which performs better than the existing methods. Statistical inference is the process of reasoning from observed data back to its underlying mechanism. Shrinkage and empirical Bayes methods provide useful techniques for combining data from various sources.  B.  Efron (Newsletter of the Royal Statistical Society January, 1995) predicted that shrinkage and empirical Bayes methodology would be a major area of statistical research for the early 21st century.    More recently, several authors considered a new approach to likelihood that weigh components differentially.  Interestingly, this leads to shrinkage type estimators that also feature prominently in empirical Bayes methodology.   New scientific technology, exemplified by DNA microarrays, has suddenly revived interest in these methods. These techniques will advance knowledge because of their applicability to a larger class of problems thereby extending our ability to solve advanced statistical inference problems in health-care, environmetrics, engineering and social sciences.