Geodesic
Bahadur efficiency of $\omega^2$-type criteria in the several sample case
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part IV, Tome 98 (1980), pp. 140-148 
Ya. Yu. Nikitin. Bahadur efficiency of $\omega^2$-type criteria in the several sample case. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part IV, Tome 98 (1980), pp. 140-148. http://geodesic.mathdoc.fr/item/ZNSL_1980_98_a10/
@article{ZNSL_1980_98_a10,
     author = {Ya. Yu. Nikitin},
     title = {Bahadur efficiency of $\omega^2$-type criteria in the several sample case},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {140--148},
     year = {1980},
     volume = {98},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1980_98_a10/}
}
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We consider the problem of testing of the hypothesie that $r$ independent samples of sizes $n_1,n_2,\dots,n_r$, are drawn from the some population with continuous distribution function $F$. We obtain the local exact slope in the Bahadur sense of the statistic $$ \omega^k_{n_1,n_2,\dots,n_r;q}=\sum_{j=1}^r\rho_j^{k/3} \int_{-\infty}^\infty[F_{n_j}^{(j)}(t)-F(t)]^kq(F(t))\,dF(t), $$ where $F_{n_j}^{(j)}(t)$ are ampirical distribution functions, $q$ is a weight function, $k$ a natural number.