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

这个美国-捷克斯洛伐克研究项目安德鲁博士 巴尔的摩县马里兰州大学的Rukhin和Dr. 信息理论自动化研究所的伊戈尔·瓦伊达， 捷克斯洛伐克科学院，将重点研究两个问题 与信息论和统计决策论相关的：（1） 变点估计问题;（2）自适应分类 随机过程的问题 第一个问题涉及 经典的两点间变点估计问题 分布。 引入了渐近有效性的概念 尽管没有一致的变点估计器。 研究人员将研究新的最优性度量， 研究自适应估计的存在性， 渐近有效的，当一个滋扰参数存在。 一 这个问题的随机过程的版本，其中一致 估计器存在也将被处理。 在第二个问题中， Rukhin和Wajda博士将对随机 处理成给定分布的族（时间可以是离散的， 连续的）。 他们必须推导出一个新的误差不等式 任何分类规则的概率。 这种不平等导致了 渐近最优性的概念比经典的更一般。 他们将获得适应性存在的条件 分类程序。 本项目在统计和概率履行程序 促进科学知识的目标， 美国和东欧的专家将联合收割机 优势互补，资源共享 兴趣和能力。

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.