Mathematical Sciences: Problems in Mathematical Statistics

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This research will be done by four investigators. The first investigator will study the consistency, rates of convergence, distribution theory and finite-sample properties of a class of nonparametric change-point estimators. He will also investigate the asymptotic distribution theory of degenerate U-statistics computed from dependent data and compare three nonparametric confidence interval techniques which are based upon subseries values of a general statistics from a stationary sequence. The second investigator will study aspects of smoothing methods, location dependent smoothing, smoothing techniques applied to model selection, classification, bandwidth and kernel selection and hazard functions. The third investigator will study several estimators of data transformation to normality or to symmetry and homoscedasticity, generation of efficient nonlinear experimental design by stochastic approximation and jointly with the fourth investigator, he will look at nonparametric sequential age replacement policies. The last investigator will study the strategic implecations of using the Ascombe-Colton model for sequential clinical trials, as apposed to the standard Neyman-Pearson model. He will also continue to study approximation methods for optimal stopping problemsand distributional questions for some functionals of Brownian motion, of statistical interest.