# Uniform hypothesis testing for finite-valued stationary processes

* Auteur correspondant
1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : Given a discrete-valued sample $X_1,\dots,X_n$ we wish to decide whether it was generated by a distribution belonging to a family $H_0$, or it was generated by a distribution belonging to a family $H_1$. In this work we assume that all distributions are stationary ergodic, and do not make any further assumptions (e.g. no independence or mixing rate assumptions). We would like to have a test whose probability of error (both Type I and Type II) is uniformly bounded. More precisely, we require that for each $\epsilon$ there exist a sample size $n$ such that probability of error is upper-bounded by $\epsilon$ for samples longer than $n$. We find some necessary and some sufficient conditions on $H_0$ and $H_1$ under which a consistent test (with this notion of consistency) exists. These conditions are topological, with respect to the topology of distributional distance.
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Article dans une revue
Statistics, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2014, 48 (1), pp.121-128. 〈10.1080/02331888.2012.719511〉
Domaine :

Littérature citée [14 références]

https://hal.inria.fr/inria-00610009
Contributeur : Daniil Ryabko <>
Soumis le : vendredi 26 décembre 2014 - 23:39:33
Dernière modification le : jeudi 21 février 2019 - 10:52:49
Document(s) archivé(s) le : vendredi 27 mars 2015 - 13:50:10

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Daniil Ryabko. Uniform hypothesis testing for finite-valued stationary processes. Statistics, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2014, 48 (1), pp.121-128. 〈10.1080/02331888.2012.719511〉. 〈inria-00610009v2〉

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