Mathematical Sciences: Probabilistic Limit Theorems and Applications

调查员将进行实证研究 过程，U过程，它们的引导程序和一些 在统计中的应用。 退化U-的极限理论 进程尚未达到令人满意的阶段， 无论退化与否，U-过程的bootstrap都远未实现 解决了 应用包括渐近理论以及 经验单纯形的唯一性和鲁棒性 中位数 U统计的开放性问题，例如几乎肯定 随机变量正规化乘积和的零收敛性 还将考虑变量。 现代经验过程理论，发展于上个世纪， 二十年，尚未完全完成，不仅揭示了 统计学中的一个基本问题（即， 样本属性接近人口属性），但 提供了一个高的道路，研究的重要问题， 渐近统计U-过程，非线性推广 经验过程，应该发挥类似的作用，虽然更多 限制，角色。我们建议继续进行经验和 U-进程及其引导程序，并研究一些 应用，如多维鲁棒定位 参数

The investigator will conduct research on empirical processes, U-processes, their bootstrap and some of their applications in statistics. The limit theory for degenerate U- processes has not yet reached a satisfactory stage, and the bootstrap of U-processes, degenerate or not, is far from being resolved. The applications include asymptotic theory as well as uniqueness and robustness properties of the empirical simplicial median. Open questions for U-statistics, such as almost sure convergence to zero of sums of normalized products of random variables will also be considered. Modern empirical process theory, developed during the last twenty years and not yet totally completed, not only sheds light on one of the basic questions in Statistics (namely, how well do sample properties approach population properties) but has been providing a high road to the study of important problems in asymptotic statistics. U--processes, a non-linear generalization of empirical processes, should play a similar, although more restricted, role. We propose to continue work on empirical and U--processes and their bootstraps, and to investigate some applications, such as to multidimensional robust location parameters.