Mathematical Sciences: Adaptive Statistical Procedures

点击翻译按钮获取中文摘要

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.