Mathematical Sciences: Topics in Statistical Theory

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Professor Berk will focus on testing for interaction in a two-way table with unbalanced data, a problem that has no satisfactory distribution-free solution to date. Professor Singh will continue work on resampling methods by introducing the idea of ranking directional data in the order of centrality. This ranking provides a natural concept of the median on a sphere. He will also work on asymptotic lower bounds of efficiency for estimators and adaptive estimation. Professor Liu pursues questions related to the notion of simplicial depth. Several topics in statistical theory will be investigated. The potential impact includes a broadening of the applicability of statistical methods for categorical data and for sparse data structures.