Geodesic
On the distribution of the statistic of the most powerful test in compound Markov chains
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 4, pp. 741-746

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The paper deals with a sequence of outcomes realized after $n$ tests, connected into a compound Markov chain of order $s-1$ with $k$ states and with the transition probabilities of the form $1/k+\alpha/k\varphi(k)$ where $\varphi(k)$ as $k\to\infty$ and $|\alpha|$. The statistic of the most powerful test for two simple hypotheses concerning the values of $\alpha$ is considered and some asymptotic properties of this statistic are studied as $n$, $k\to\infty$. 
@article{TVP_1967_12_4_a13,
     author = {P. F. Belyaev},
     title = {On the distribution of the statistic of the most powerful test in compound {Markov} chains},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {741--746},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_4_a13/}
}
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P. F. Belyaev. On the distribution of the statistic of the most powerful test in compound Markov chains. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 4, pp. 741-746. http://geodesic.mathdoc.fr/item/TVP_1967_12_4_a13/