Mathematical Sciences: Mathematical Statistics

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This project involves basic research into the mathematical properties of statistical procedures. Of special interest are questions of admissibility of common parametric estimators. For example, the least squares estimator of a regression parameter or of such a parameter after selection based on the data will be studied. Also of interest are the conditional properties of such estimators and related confidence procedures, non-parametric estimates of density function, (nearly) distribution free confidence bands and tests for multivariate distribution functions. This research in statistics focuses on the mathematical properties of estimators. Insight derived from this research will assist the development of statistical methodologies and improve the application of statistics in many scientific fields.