PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Discrimination between B-processes is impossible
Daniil Ryabko
Journal of Theoretical Probability Volume 23, Number 2, pp. 565-575, 2010. ISSN 0894-9840

Abstract

Two series of binary observations x1, x1, . . . and y1, y2, . . . are presented: xn and yn are given at each time n ∈ N. It is assumed that the sequences are generated independently of each other by two B-processes. The question of interest is whether the sequences represent a typical realization of two different processes or of the same one. It is demonstrated that this is impossible to decide, in the sense that every discrimination procedure is bound to err with non-negligible frequency when presented with sequences from some B-processes. This contrasts with earlier positive results on B-processes, in particular, those showing that there are consistent ¯ d-distance estimates for this class of processes, and on ergodic processes, in particular, those establishing consistent change point estimates.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
ID Code:5977
Deposited By:Daniil Ryabko
Deposited On:08 March 2010