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.

马里兰州大学巴尔的摩县的安德鲁·鲁金博士和捷克斯洛伐克科学学院信息理论与自动化研究所的伊戈尔·瓦吉达博士之间的美国 - 捷克斯洛伐克研究项目将集中在相对于信息和统计决策的两个问题上理论：（1）变更点估计问题； （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化点的经典估计问题。 尽管没有一致的变更点估计器，但仍引入了渐近效率的概念。 研究人员将研究新的最佳措施，并研究存在滋扰参数时完全渐近效率的自适应估计量的存在。 也将解决存在一致估计量的随机过程的此问题。 在第二个问题中，博士。 Rukhin和Wajda将将随机过程实现为给定分布的家族（时间可以离散或连续）。 他们必须为任何分类规则的错误概率得出新的不等式。 这种不平等导致的渐近最优性概念比经典的概念更笼统。 他们将获得存在自适应分类程序的条件。 该项目在统计和概率方面实现了计划的目标，即通过使美国和东欧的主要专家能够将互补才能和资源汇集在具有强大的共同利益和能力的领域的资源中，以推进科学知识。