An impossibility result for process discrimination
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Limits to consistent on-line forecasting for ergodic time series
IEEE Transactions on Information Theory
The interactions between ergodic theory and information theory
IEEE Transactions on Information Theory
An impossibility result for process discrimination
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Nonparametric statistical inference for ergodic processes
IEEE Transactions on Information Theory
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Two series of binary observations x1, x1,... and y1, y2,... are presented: at each time n ∈ N we are given xn and yn. It is assumed that the sequences are generated independently of each other by two stochastic processes. We are interested in the question of whether the sequences represent a typical realization of two different processes or of the same one. We demonstrate that this is impossible to decide in the case when the processes are B-processes. It follows that discrimination is impossible for the set of all (finite-valued) stationary ergodic processes in general. This result means that every discrimination procedure is bound to err with non-negligible frequency when presented with sequences from some of such processes. It contrasts earlier positive results on B-processes, in particular those showing that there are consistent d-distance estimates for this class of processes.