Mathematical Sciences: Mathematical Statistics

这个项目涉及对统计程序的数学性质的基础研究。特别感兴趣的是常见参数估计量的可容许性问题。例如，将研究回归参数或基于数据选择后的参数的最小二乘估计器。这些估计量的条件性质和相关的置信度程序、密度函数的非参数估计、(几乎)分布自由置信带和多元分布函数的检验也令人感兴趣。统计学的研究主要集中在估计量的数学性质上。这项研究得出的见解将有助于发展统计方法，并改进统计学在许多科学领域的应用。

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.