U.S.-Czechoslovakia Research on Information Theory and Mathematical Statistics

美捷信息论与数理统计研究

• 批准号: 9214474
• 负责人: Andrew Rukhin
• 金额: $ 1.2万
• 依托单位: University of Maryland Baltimore County
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-02-01 至 1996-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9214474&HistoricalAwards=false
• 关键词: U.S.; Czechoslovakia; Research; Information; Theory

This U.S.-Czechoslovakia research project between Dr. Andrew Rukhin of the University of Maryland, Baltimore County and Dr. Igor Wajda of the Institute of Information Theory & Automation, Czechoslovak Academy of Sciences, will focus on two problems relative to information theory and statistical decision theory: (1) Change-point estimation problem; and (2) Adaptive classification problems for stochastic process. The first problem deals with the classical estimation problem of change-point between two different distributions. A notion of asymptotic efficiency is introduced despite there being no consistent estimator of the change-point. The researchers will investigate the new optimality measure and study the existence of adaptive estimators which are fully asymptotic efficient, when a nuisance parameter is present. A version of this problem for stochastic processes in which consistent estimators exist will also be addressed. In the second problem, Drs. Rukhin and Wajda will classify a realization of a stochastic process into a family of given distributions (time can be discrete or continuous). They have to derive a new inequality for the error probability of any classification rule. This inequality leads to a notion of asymptotic optimality more general than the classical one. They will obtain conditions for the existence of adaptive classification procedures. This project in statistics and probability fulfills the program objective of advancing scientific knowledge by enabling leading experts in the United States and Eastern Europe to combine complementary talents and pool resources in areas of strong mutual interest and competence.

巴尔的摩县马里兰大学的Andrew Rukhin博士和捷克斯洛伐克科学院信息理论与自动化研究所的Igor Wajda博士开展的这一美国-捷克斯洛伐克研究项目将集中于与信息论和统计决策理论相关的两个问题：(1)变点估计问题；(2)随机过程的自适应分类问题。第一个问题涉及两个不同分布之间变点的经典估计问题。引入了渐近有效性的概念，尽管对变点没有一致的估计器。研究人员将研究新的最优性度量，并研究当干扰参数存在时，完全渐近有效的自适应估计器的存在性。对于存在相容估计量的随机过程，也将讨论这个问题的一个版本。在第二个问题中，Rukhin和Wajda博士将随机过程的实现分类为一族给定的分布(时间可以是离散的，也可以是连续的)。他们必须为任何分类规则的错误概率推导出一个新的不等式。这个不等式导致了一个比经典的渐近最优性更普遍的概念。他们将获得自适应分类程序存在的条件。这个统计和概率项目通过使美国和东欧的顶尖专家能够将互补的人才结合在一起，并在相互感兴趣和能力很强的领域汇集资源，从而实现了促进科学知识的计划目标。