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