A criterion for hypothesis testing for stationary processes - Inria - Institut national de recherche en sciences et technologies du numérique
Rapport (Rapport De Recherche) Année : 2009

A criterion for hypothesis testing for stationary processes

Résumé

Given a finite-valued sample $X_1,\dots,X_n$ we wish to test whether it was generated by a stationary ergodic process belonging to a family $H_0$, or it was generated by a stationary ergodic process outside $H_0$. We require the Type I error of the test to be uniformly bounded, while the type II error has to be mande not more than a finite number of times with probability 1. For this notion of consistency we provide necessary and sufficient conditions on the family $H_0$ for the existence of a consistent test. This criterion is illustrated with applications to testing for a membership to parametric families, generalizing some existing results. In addition, we analyze a stronger notion of consistency, which requires finite-sample guarantees on error of both types, and provide some necessary and some sufficient conditions for the existence of a consistent test. We emphasize that no assumption on the process distributions are made beyond stationarity and ergodicity.
Fichier principal
Vignette du fichier
1c.pdf (161.29 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

inria-00389689 , version 1 (29-05-2009)
inria-00389689 , version 2 (30-05-2009)
inria-00389689 , version 3 (19-10-2009)
inria-00389689 , version 4 (26-12-2014)

Identifiants

  • HAL Id : inria-00389689 , version 3
  • ARXIV : 0905.4937

Citer

Daniil Ryabko. A criterion for hypothesis testing for stationary processes. [Research Report] 2009. ⟨inria-00389689v3⟩

Collections

LIFL
310 Consultations
211 Téléchargements

Altmetric

Partager

More