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

美国-捷克斯洛伐克研究项目由巴尔的摩马里兰大学的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博士共同完成，将重点研究与信息理论和统计决策理论相关的两个问题：(1)变点估计问题；(2)随机过程自适应分类问题。第一个问题处理两个不同分布之间变点的经典估计问题。在没有相合估计的情况下，引入了渐近效率的概念。研究者将研究新的最优性度量，并研究当存在扰值参数时完全渐近有效的自适应估计的存在性。对于存在一致估计量的随机过程，也将讨论这个问题的一个版本。在第二个问题中，dr。Rukhin和Wajda将随机过程的实现分类为一系列给定的分布（时间可以是离散的或连续的）。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。这个不等式引出了一个比经典的渐近最优性更普遍的概念。他们将获得存在自适应分类程序的条件。该统计与概率项目通过使美国和东欧的顶尖专家在共同感兴趣和能力强的领域结合互补的人才和汇集资源，实现了推进科学知识的计划目标。

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.