Title :

Uniform hypothesis testing for finite-valued stationary processes

Author(s) :

Ryabko, Daniil [Auteur correspondant]
Sequential Learning [SEQUEL]

Journal title :

Statistics

Pages :

121-128

Publisher :

Taylor & Francis: STM, Behavioural Science and Public Health Titles

Publication date :

2014

ISSN :

0233-1888

English keyword(s) :

property testing
stationary processes
ergodic time series
hypothesis testing

HAL domain(s) :

Mathématiques [math]/Statistiques [math.ST]
Statistiques [stat]/Théorie [stat.TH]
Informatique [cs]/Théorie de l'information [cs.IT]
Mathématiques [math]/Théorie de l'information et codage [math.IT]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL