A criterion for hypothesis testing for stationary processes

Daniil Ryabko 1, 2
2 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal, Inria Lille - Nord Europe
Abstract : 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.
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  • HAL Id : inria-00389689, version 4
  • ARXIV : 0905.4937

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Daniil Ryabko. A criterion for hypothesis testing for stationary processes. [Research Report] INRIA Lille. 2009. 〈inria-00389689v4〉

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