Geodesic
On asymptotic efficiency and local
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 219-231

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Many well-known homogeneity tests are based on two-sample $U$- and $V$-statistics. Using their large deviation asymptotics we calculate for them the local Bahadur efficiency for common alternatives and find general conditions of their local asymptotic optimality. 
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     title = {On asymptotic efficiency and local},
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V. V. Litvinova; Ya. Yu. Nikitin. On asymptotic efficiency and local. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 219-231. http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a10/