## On the converse theorem in statistical hypothesis testing for Markov chains.(English)Zbl 0788.62008

This work is a continuation of the authors’ earlier work, ibid., 623-628 (1993; Zbl 0780.62005), on the converse theorem in statistical hypothesis testing. Here hypothesis testing for two Markov chains is considered. Under the constraint that the first-kind error probability is less than or equal to $$\exp(-rn)$$, where $$r$$ is a given positive number, the second-kind error probability is minimized. The geodesic that connects the two Markov chains is defined. By analyzing the geodesic, the so- called power exponents are calculated and then represented in terms of Kullback-Leibler divergence.

### MSC:

 62B10 Statistical aspects of information-theoretic topics 62M02 Markov processes: hypothesis testing 62A01 Foundations and philosophical topics in statistics 62F03 Parametric hypothesis testing

Zbl 0780.62005
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