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.
