Geodesic
Asymptotically minimax criteria for testing non-parametric hypotheses on the probability density
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 8, Tome 166 (1988), pp. 44-53

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Asymptotically minimax tests for testing of nonparametric hypothesis concerning density functions and also for testing of symmetry, homogenity, independence is obtained. 
@article{ZNSL_1988_166_a5,
     author = {M. S. Ermakov},
     title = {Asymptotically minimax criteria for testing non-parametric hypotheses on the probability density},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {44--53},
     publisher = {mathdoc},
     volume = {166},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_166_a5/}
}
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M. S. Ermakov. Asymptotically minimax criteria for testing non-parametric hypotheses on the probability density. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 8, Tome 166 (1988), pp. 44-53. http://geodesic.mathdoc.fr/item/ZNSL_1988_166_a5/