Mathematical Sciences: Sequential Inference, Admissibility, and Invariance

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Research will be conducted in several areas of statistics: (1) Marden will work on nonnull models for rank statistics and the development of new rank procedures; (2) Martinsek will work on sequential models for determining the estimator as well as the sample size in location and regression models; comparison of slope estimates in adaptive stochastic approximation; and asymptotically optimal procedures in multistage estimation; (3) Stout's research will be on probabilistic modeling and statistical analysis for interesting data structures, including those found in multiple item response tests and where there are latent variables; (4) Wijsman's research will include the study of sequential confidence sets and develop a method of using cross sections to deriving distributions in models that admit invariance transformations. This research in the general area of statistics aims to come to grips with a broad variety of mathematical and methodological problems that have been encountered in current efforts to extend statistics to a broader variety of applications. Included are major thrusts to develop sequential methods for analyzing data, with the potential for saving resources in scientific experimentation.