inria-00319076, version 7
An impossibility result for process discrimination
(2008)
Résumé : Two series of binary observations $x_1,x_1,\dots$ and $y_1,y_2,\dots$ are presented: at each time $n\in\N$ we are given $x_n$ and $y_n$. It is assumed that the sequences are generated independently of each other by two B-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 sense that every discrimination procedure is bound to err with non-negligible frequency when presented with sequences from some B-processes. This contrasts earlier positive results on B-processes, in particular those showing that there are consistent $\bar d$-distance estimates for this class of processes.
- a – INRIA
- 1 : SEQUEL (INRIA Lille - Nord Europe)
- INRIA – CNRS : UMR8022 – CNRS : UMR8146 – Université Lille 1 - Sciences et Technologies – Université Charles de Gaulle - Lille III – Ecole Centrale de Lille
- Domaine : Mathématiques/Probabilités
Mathématiques/StatistiquesStatistiques/ThéorieInformatique/Théorie de l'information et codageMathématiques/Théorie de l'information et codage - Mots-clés : Process discrimination – B-processes – stationary ergodic processes – time series – homogeneity testing
- Versions disponibles : v1 (05-09-2008) v2 (11-01-2009) v3 (12-01-2009) v4 (09-05-2009) v5 (09-05-2009) v6 (10-05-2009) v7 (10-07-2009)
- inria-00319076, version 7
- http://hal.inria.fr/inria-00319076
- oai:hal.inria.fr:inria-00319076
- Contributeur : Daniil Ryabko
- Soumis le : Vendredi 10 Juillet 2009, 11:30:56
- Dernière modification le : Vendredi 10 Juillet 2009, 11:34:17
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