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We study the LRT statistic for testing
a single population i.i.d. model against a mixture of two populations with Markov regime.
We prove that
the LRT statistic converges to infinity in probability
as the number of observations tends to infinity.
This is a consequence of a convergence result
of the LRT statistic for a subproblem where the parameters
are restricted to a subset of the whole parameter set.
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