Mathematical Sciences: Adaptive Statistical Procedures

Rukhin将致力于自适应统计程序，当使用大偏差概率作为性能标准时，这些程序是相关的。在假设检验的情况下，Rukhin计划获得自适应检验存在的条件，即，对于未知干扰参数的任何固定值，该检验是完全渐近Bahadur有效的，并且使得检验独立于该参数值。将导出自适应测试统计量的形式，并探索其在中等样本大小下的行为。类似的问题将在无穷维扰动参数存在的情况下估计向量参数的问题中进行研究。将研究递归分类程序，并将获得改进的可靠性分位数估计器。统计学领域的这项工作的重点是解决一些问题，这些问题将使假设检验程序适应积累的信息。在这些问题上的成功将有助于了解如何优化科学实验的性能。

Rukhin will work on adaptive statistical procedures which are relevant when probabilities of large deviations are used as a performance criterion. In a hypothesis testing situation, Rukhin plans to obtain conditions for the existence of an adaptive test, i.e., a test which is fully asymptotically Bahadur efficient for any fixed value of an unknown nuisance parameter and such that the test is independent of this parameter value. The form of the adaptive test statistics will be derived, and their behavior for moderate sample sizes will be explored. Similar questions will be investigated in the problem of estimating a vector parameter in the presence of an infinite-dimensional nuisanceparameter. Recurrent classification procedures will be studied and improved reliability quantile estimators will be obtained. This work in the field of statistics focuses on solving problems that will adapt hypotheses testing procedures to information as it accummulates. Success on these problems will contribute to the knowledge of how to optimize the performance of scientific experimentation.