Mathematical Sciences: Statistical Theory and Methodology

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This research project involves a team of scholars involved in the following topics: (1) applications of group representations, (2) Bayesian statistics, (3) rates of convergence of Markov chains to their stationary distributions, (4) regression percentiles using an asymmetric least squares loss function, (5) using compliance as a covariate in a randomized clinical trial, (6) influence functions for confidence limits, (7) better automatic confidence intervals for parametric problems, (8) permutation tests for 'messy situations', (9) minimax estimation, (10) loss and risk estimation, (11) volumes of tubular neighborhoods and statistical applications, (12) maximum entropy methods, (13) confidence regions in semilinear regression, (14) change-point problems, (15) sequential tests and estimates, (16) the approximate evaluation of expectations, (17) bootstrap confidence intervals in complex models, (18) bootstrap choice of tuning parameters and adaptation, and (19) approximate inference for parametric models via least favorable families. The general aim of this project is the development of new statistical theory and methodology of interest to applied mathematics. The research involves a combination of traditional mathematical statistics and modern computational methods. Particular goals are understanding more complicated models than are traditionally used and automating insofar as possible statistical procedures for routine use.