Geodesic
On uniform consistency of nonparametric tests
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 98-147

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We provide necessary and sufficient conditions of uniform consistency of nonparametric sets of alternatives for widespread nonparametric tests. Nonparametric sets of alternatives can be defined both in terms of distribution function and density (or signals in the problem of signal detection in Gaussian white noise). 
@article{ZNSL_2019_486_a6,
     author = {M. S. Ermakov},
     title = {On uniform consistency of nonparametric tests},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {98--147},
     publisher = {mathdoc},
     volume = {486},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a6/}
}
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M. S. Ermakov. On uniform consistency of nonparametric tests. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 98-147. http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a6/