PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Testing composite hypotheses about discrete-valued stationary processes
Daniil Ryabko
In: ITW 2010, 6-8 January 2010, Cairo, Egypt.


Given a discrete-valued sample X1; : : : ;Xn we wish to test whether it was generated by a stationary ergodic process belonging to a family H0, or it was generated by a stationary ergodic process outside H0. Apart from the assumptions of stationarity and ergodicity, no further probabilistic or parametric assumptions are made. We require the Type I error of the test to be uniformly bounded, while the probability of Type II error has to tend to zero as the sample size increases. For this notion of consistency we provide necessary and sufficient conditions on the family H0 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.

EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:5980
Deposited By:Daniil Ryabko
Deposited On:08 March 2010